CN102314559B - Method for predicting retention time of gas phase chromatogram based on macromolecule crystallization behavior derivation retention equation - Google Patents

Abstract

The invention discloses a method for predicting retention time of a gas phase chromatogram based on a macromolecule crystallization behavior derivation retention equation. The method comprises the following processes: deducing a retention equation curve which contains temperature and capacity factors based on macromolecule crystallization behavior, wherein the curve can be set up by only using three known data points which contain temperature and capacity factors of a compound at corresponding temperature; setting virtual dead time for a chromatographic column at a random temperature point according to measured retention time at a constant temperature; determining the capacity factor of the compound at the random temperature point through differentiating and integrating the whole chromatographic column according to the set retention equation curve; and predicting the retention time of the compound on the chromatographic column under a temperature-programming condition by using the data, and comparing the predicted retention time with an actually-measured value. The method for predicting the retention time of the gas phase chromatogram based on the macromolecule crystallization behavior derivation retention equation disclosed by the invention has the following advantages that: the number of adopted data points is few, and the number of experiments is reduced; the dead time has no need of measuring, and the process for predicting is simplified; and the predicting accuracy is high, and the application range is wide.

Description

By polymer crystallization behavior derivation retention equation prediction gas chromatography retention time method

Technical field

The present invention relates to a kind of method based on polymer crystallization behavior derivation retention equation prediction gas chromatography retention time, belong to gas chromatographic technique field.

Background technology

It is a technology very efficiently that gas chromatography forms for compartment analysis complex compound.But for boiling point, form the very large complicated ingredient of variation range, select suitable temperature programming chromatography separation condition conventionally to waste time and energy.By calculating, predict the retention time of sample component under any temperature programme condition, can avoid blindly changing by rule of thumb separation condition, reducing experiment number, and comparatively fast filter out optimum temperature rise program, thereby realize the Automatic Optimal processing of chromatographic condition.

People, when the Changing Pattern of scientific research and description things, always wish to use the simplest mathematical formulae to express.Mathematical formulae is simpler, and required definite parameter is just fewer, and this just means the whole parameters that only just can obtain formula with a small amount of experimental data point; If but mathematical formulae is too simple, certainly will there is deviation to the simulation of real change trend, will have influence on the accuracy of prediction.Therefore, in the forecasting process of gas chromatography retention time, how to set up the retention equation form of multiparameter, make retention equation can accurately simulate capacity factor measure variation with temperature trend, not because too much parameter increases experiment burden, significant for the accurately predicting of retention time again.

According to investigation and literature search, 3 data points that comprise the capacity factor measure at temperature temperature corresponding to compound of many employings are set up retention equation both at home and abroad, but data point is less owing to adopting, the retention equation that simulation is set up is comparatively obvious with the retention equation deviation that experiment obtains, and makes the predicated error of retention time bigger than normal.

The crystallization relation of high molecular polymer is that straight-line equation can be set up by the data point of 2 crystallinity that comprise polymkeric substance and corresponding density by linear relationship between the crystallinity of polymkeric substance and corresponding density.And straight-line equation is added to the coefficient that is greater than 1, can make straight line change convex curve into, then carry out the concave curve that serial conversion can form monotone decreasing.Thus, only utilize 3 data points that comprise capacity factor measure at temperature temperature corresponding to compound, just can set up retention equation, thereby be used for predicting retention time.

Summary of the invention

The object of the present invention is to provide a kind of method of predicting gas chromatography retention time based on polymer crystallization behavior derivation retention equation.By the retention time of the method prediction gas chromatography temperature programme, not only forecasting process is simple, and precision of prediction is high.

The present invention is realized by the following technical programs, a kind of method based on polymer crystallization behavior derivation retention equation predictor intensification retention time, the method is for HP6890 gas chromatograph and nonpolar HP-5 chromatographic column (hereinafter to be referred as chromatographic column), with described polymer crystallization behavior derivation retention equation, predict gas chromatography retention time, it is characterized in that comprising following process:

The first step, the retention equation curve of deriving and containing temperature, capacity factor measure based on polymer crystallization behavior:

(1) according to the crystallinity of high molecular polymer and the linear variation relation of density, during the complete crystallization of superpolymer, density is maximum, and its density is ρ _c, crystallinity

and complete when non-crystallizable density minimum, its density is ρ _a, crystallinity

in the density of other crystalline states between minimum and maximum; The crystallinity formula of superpolymer is by point (ρ _a, 0%) and point (ρ _c, 100%) just can determine, as shown in Equation 1:

formula 1

In formula 1:

for the crystallinity of superpolymer, ρ is corresponding density, ρ _cdensity during for the complete crystallization of superpolymer,

ρ _afor complete density when non-crystallizable of superpolymer, and have and be related to 0 < ρ _a≤ ρ≤ρ _c;

By formula 1, can be obtained

as shown in Equation 2:

formula 2

(2), because compound is in HP-5 chromatographic column, capacity factor measure variation with temperature non-rectilinear relation, but the concave curve relation of monotone decreasing, for linear formula 2 is become to curve, need to be multiplied by ρ to formula 2 equation right-hand members _cbe out of shape with the coefficient that is compared to of ρ, become formula 3:

formula 3

Formula 3 is carried out to differentiate, and first order derivative is greater than 0, second derivative is less than 0, and formula 3 is monotonically increasing convex curve; Arrangement formula 3 obtains formula 4:

formula 4

For formula 4 being become to the concave curve of monotone decreasing, introduce parameter χ, and order

substitution formula 4 obtains formula 5:

formula 5

The function that formula 5 is constructed is through (ρ _a, 1) and (ρ _c, 0) and two end points, and field of definition ρ > 0; Formula 5 is carried out to differentiate, and first order derivative is less than 0, second derivative is greater than 0, the concave curve that formula 5 is monotone decreasing; Formula 5 is converted to deriving 6:

$\mathrm{\&rho;}=\frac{{\mathrm{\&rho;}}_a\&CenterDot;{\mathrm{\&rho;}}_c}{{\mathrm{\&rho;}}_a+({\mathrm{\&rho;}}_c-{\mathrm{\&rho;}}_a)\&CenterDot;\mathrm{\&chi;}}$ Formula 6

(3) in order to utilize the retention time of the crystallinity behavior prediction gas chromatography of superpolymer, the χ in formula 6, ρ need to be connected with the natural logarithm lnk of temperature T, capacity factor measure respectively, be built into retention equation; Making χ is the monotonically increasing linear function of T, and through (T _a, 0) and (T _c, 1) and two point, wherein T _a< T _c, according to 2 straight line formulas, there is formula 7:

$\mathrm{\&chi;}=\frac{1}{T_c-T_a}(T-T_a)$ Formula 7

In formula 7: T _aand T _cfor known temperature, by experiment, determined, and regulation T _a< T _c;

T is unknown temperatures;

Make ρ=lnk, ρ _a=lnk _c, ρ _c=lnk _a, and formula 7 is updated in formula 6, there is formula 8:

$\ln k=\frac{{\ln k}_a\&CenterDot;{\ln k}_c}{{\ln k}_c+({\ln k}_a-{\ln k}_c)\&CenterDot;\frac{T-T_a}{T_c-T_a}}$ Formula 8

In formula 8: T _aand T _cfor known temperature, by experiment, determined, and regulation T _a< T _c;

Lnk _aand lnk _cbe respectively compound at corresponding temperature T _aand T _cunder the natural logarithm of capacity factor measure,

By experiment, determined, and set lnk _c< lnk _a;

T is unknown temperatures, and lnk is the natural logarithm of the capacity factor measure of compound under corresponding temperature T;

Formula 8 is through point (lnk _a, T _a) and point (lnk _c, T _c) the monotone decreasing concave curve of lnk to T, wherein the span of lnk is to be greater than 0 positive number; But due in gas chromatography, the lnk of compound can just can bear, therefore by lnk, lnk _aand lnk _call add non-negative parameter lambda, guarantee lnk+ λ, lnk _a+ λ and lnk _c+ λ value is positive number, can obtain formula 9 by formula 8:

$\ln k+\mathrm{\&lambda;}=\frac{({\ln k}_a+\mathrm{\&lambda;})\&CenterDot;({\ln k}_c+\mathrm{\&lambda;})}{({\ln k}_c+\mathrm{\&lambda;})+[({\ln k}_a+\mathrm{\&lambda;})-({\ln k}_c+\mathrm{\&lambda;})]\&CenterDot;\frac{T-T_a}{T_c-T_a}}$ Formula 9

Arrangement formula 9 obtains formula 10 and formula 11:

$\ln k=\frac{({\ln k}_a+\mathrm{\&lambda;})\&CenterDot;({\ln k}_c+\mathrm{\&lambda;})}{({\ln k}_c+\mathrm{\&lambda;})+({\ln k}_a-{\ln k}_c)\&CenterDot;\frac{T-T_a}{T_c-T_a}}-\mathrm{\&lambda;}$ Formula 10

$\mathrm{\&lambda;}=\frac{{\ln k}_c\&CenterDot;(\ln k-{\ln k}_a)+\ln k\&CenterDot;({\ln k}_a-{\ln k}_c)\&CenterDot;\frac{T-T_a}{T_c-T_a}}{({\ln k}_a-\ln k)-({\ln k}_a-{\ln k}_c)\&CenterDot;\frac{T-T_a}{T_c-T_a}}$ Formula 11

In order to determine non-negative parameter lambda, except (lnk _a, T _a) and (lnk _c, T _c) outside 2, between 2 o'clock, increase known data point (lnk _b, T _b), by formula 11, obtain formula 12, utilize formula 12 just to obtain parameter lambda:

$\mathrm{\&lambda;}=\frac{{\ln k}_c\&CenterDot;({\ln k}_b-{\ln k}_a)+{\ln k}_b\&CenterDot;({\ln k}_a-{\ln k}_c)\&CenterDot;\frac{T_b-T_a}{T_c-T_a}}{({\ln k}_a-{\ln k}_b)-({\ln k}_a-{\ln k}_c)\&CenterDot;\frac{T_b-T_a}{T_c-T_a}}$ Formula 12

Thus, only utilize 3 known data point (lnk _a, T _a), (lnk _b, T _b) and (lnk _c, T _c) obtain λ, then λ substitution formula 10 just can be determined to retention equation, predict gas chromatography retention time; Point (lnk wherein _a, T _a) and point (lnk _c, T _c) for determining two end points of retention equation, and point (lnk _b, T _b) for determining the concavo-convex degree of retention equation curve;

Second step, the virtual dead time of setting chromatographic column arbitrary temp point:

Chromatographic column design temperature variation range is 30-250 ℃, measures compound at T ₁=30 ℃, T ₂=50 ℃, T ₃=100 ℃, T ₄=150 ℃, T ₅=200 ℃ and T ₆retention time under=250 ℃ of six constant temperature is respectively t _r1, t _r2, t _r3, t _r4, t _r5and t _r6, determine wherein minimum retention time value, to be less than any one time value of this minimum value, all can be used as virtual dead time τ;

The 3rd step, deterministic compound is in any capacity factor measure of temperature spot:

(1) according to the retention time t under measure in second step six constant temperature _r1, t _r2, t _r3, t _r4, t _r5, t _r6the virtual dead time τ having determined, employing formula 13, calculates retention factors corresponding under six constant temperature and is respectively k ₁, k ₂, k ₃, k ₄, k ₅and k ₆:

K=(t _r-τ)/τ formula 13

In formula 13: the capacity factor measure that k is compound,

τ is the virtual dead time,

T _rretention time for corresponding each temperature spot;

(2) capacity factor measure of the compound calculating in step (1) is got to natural logarithm lnk, make lnk ₁, lnk ₂, lnk ₃, lnk ₄, lnk ₅, lnk ₆with temperature T ₁, T ₂, T ₃, T ₄, T ₅, T ₆the scatter diagram changing, according to the concavo-convex distribution situation of 6 data points, therefrom selects 3 data point (lnk _a, T _a), (lnk _b, T _b) and (lnk _c, T _c), according to formula 12, obtain parameter lambda, according to formula 10, set up retention equation, thereby can deterministic compound in the capacity factor measure of temperature spot arbitrarily;

The 4th step, the temperature value of any time of determining chromatographic column in Temperature Programmed Processes:

(1) the T.T. t that determine procedures heats up and needs _total:

The T.T. t that heats up and need with formula 14 determine procedures while adopting single-order temperature programme _total:

T _total=t _h1+ t+t _h2formula 14

In formula 14: t _h1for the retention time of initial temperature, empirical value is: 1-5min;

T _h2for the retention time of the final temperature of single-order temperature programme;

T be single-order temperature programme need the time, by formula 15, calculated:

T=(T _f-T _o)/r formula 15

In formula 15: T _oinitial temperature for single-order temperature programme;

T _ffinal temperature for single-order temperature programme;

R is the heating rate of single-order temperature programme, and the experience span of r is 5-30 ℃/min;

(2) determine that mobile phase flows through the time t of whole chromatogram experience _i:

The virtual dead time τ differential of setting is become to m equal portions, and every equal portions are Δ τ:

$\mathrm{\&tau;}=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;\&tau;}$ Formula 16

In formula 16: τ is the virtual dead time, by the 3rd step, determined;

M is the umber that waits in the time interval, and it is enough large that setting value is wanted;

Δ τ is the time of every equal portions, by waiting umber m to determine;

By formula 17, determined the distance, delta l that in the time Δ τ of every equal portions, mobile phase is passed by:

Δ l=u Δ τ formula 17

In formula 17: u is column performance, is determined by formula 18:

$u=\frac{3}{32L\&CenterDot;\mathrm{\&eta;}}\&CenterDot;\frac{{{\mathrm{<figure-callout\; id="2"\; label="d\; c"\; filenames="HSA00000590338300021.png,HSA00000590338300022.png"\; state="\{\{state\}\}">d</figure-callout>}}_c}^2}{4}\&CenterDot;\frac{{(P_i^2-{P_o}^2)}^2}{(P_i^3-{P_o}^3)}$ Formula 18

In formula 18: L is column length, is determined by actual measurement;

D _cfor chromatographic column internal diameter, by actual measurement, determined;

Pi be mobile phase at the pressure of chromatographic column porch, by actual measurement, determined;

Po be mobile phase at the pressure in chromatographic column exit, by actual measurement, determined;

η is mobile phase viscosity, by actual measurement, is determined;

The distance, delta l that in the time Δ τ of every equal portions, mobile phase is passed by is carried out to integration, and the distance that mobile phase is passed by equals column length L:

$L=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;l}$ Formula 19

In formula 19: L is column length, is determined by actual measurement;

Δ l is the distance, delta l that the interior mobile phase of the time Δ τ of every equal portions is passed by, and by formula 17, is determined;

N is the distance equal portions sum that whole root chromatogram column contains;

Mobile phase is gone to the time t that time of i equal portions experiences _i:

T _i=i Δ τ formula 20

In formula 20: t _ifor mobile phase flows to the time that time of i equal portions experiences;

I is the umbers such as time;

Δ τ is the time of every equal portions, by formula 16, is determined;

(3) when deterministic compound flows to the time of i equal portions with mobile phase, the temperature T that chromatographic column is corresponding _i:

Work as t _i< t _h1, chromatographic column temperature T _i=T _o;

Work as t _h1< t _i< (t _h1+ t), chromatographic column temperature T _i=r * (t _i-t _h1)+T _o;

As (t _h1+ t)≤t _i≤ (t _h1+ t+t _h2), chromatographic column temperature T _i=T _f;

The 5th step, predict the retention time of component to be measured:

By definite T in the 4th step _iin substitution formula 10, when calculating compound and flowing to the time of i equal portions with mobile phase, namely flow to i equal portions apart from time, corresponding capacity factor measure k _i;

(1) utilize mobile phase flow to i equal portions apart from time Retention factor k corresponding to compound _i, according to formula 21 and 22, calculate respectively testing compound with mobile phase flow to i equal portions apart from time fixing mutually and the concentration of mobile phase:

K _i* β=C _sni/ C _mniformula 21

C _mni+ C _sni=C _niformula 22

In formula 21: β is chromatographic column self compare numerical value, be known number;

C _mniand C _snibe respectively mobile phase flow to i equal portions apart from time, testing compound is mobile phase and fixing concentration in mutually in n equal portions distance;

In formula 22: C _nifor mobile phase flow to i equal portions apart from time, the total concentration of testing compound in n equal portions distance, it is determined by formula 23 and formula 24:

C _ai=C _{s (n-1) i}+ C _{m (n-1) (i-1)}formula 23

C _m00=1 μ g/ml formula 24

In formula 23 and formula 24:

C _m00for the concentration of the initial sample introduction of component,

C _{s (n-1) i}for mobile phase flow to i equal portions apart from time, compound is in the fixing concentration of Xiangli of n equal portions distance;

C _{m (n-1) (i-1)}for mobile phase flow to i-1 equal portions apart from time, the concentration of compound in the mobile phase of n-1 equal portions distance;

(2) determining of testing compound retention time:

According to (1) of the 5th step, by computing machine calculate obtain mobile phase flow to i-1, i and i+1 equal portions apart from time, last equal portions distance of chromatographic column N equal portions apart from, testing compound is respectively C in the concentration of mobile phase _{mN (i-1)}, C _mNiand C _{mN (i+1)}, three concentration are compared:

Work as C _{mN (i-1)}< C _mNi> C _{mN (i+1)}time, stop calculating, while being i by formula 20 calculating equal portions apart from number, the time t needing altogether _i, this time is retention time;

When not meeting above-mentioned inequality C _{mN (i-1)}< C _mNi> C _{mN (i+1)}time, continue to repeat above-mentioned calculating, until reach, meet inequality C _{mN (i-1)}< C _mNi> C _{mN (i+1)}till, determine retention time.

The invention has the advantages that: by being nonlinear retention equation by linear polymer crystallization degree relation derivation, only utilize 3 data points that comprise capacity factor measure at temperature temperature corresponding to compound just can carry out the prediction of retention time, and because the process of prediction retention time can be set the dead time arbitrarily and not need to calculate the dead time, not only reduced experiment number but also simplified forecasting process, prediction retention time precision is high, makes this invention have the scope of application comparatively widely.

Accompanying drawing explanation

Fig. 1 is the rolling schedule figure that the present invention is based on polymer crystallization behavior derivation retention equation prediction gas chromatography retention time.

When Fig. 2, Fig. 3, Fig. 4 are respectively virtual dead time 1.85min, the capacity factor measure of methyl alcohol, heptane, isoamyl acetate and temperature relation scatter diagram.

Embodiment

Embodiment 1

Instrument: HP6890 gas chromatograph, flame ionization ditector, 6890 gas chromatography workstations;

Chromatographic column: nonpolar HP-5 chromatographic column (5% phenyl methyl polysiloxane, 30m * 0.32mm * 0.25 μ m, Anjelen Sci. & Tech. Inc);

Condition: the temperature of detecting device is 250 ℃, injector temperature is 250 ℃;

Carrier gas: use high pure nitrogen (purity is not less than 99.999%);

Input mode: split sampling, split ratio is 50: 1, and each sample size is 0.2ul, and concentration is 1 μ g/ml;

Constant current operation pattern: i.e. carrier gas is at column outlet place, and it is constant that mass rate keeps, and is 1.0ml/min;

Select three different temperature programmes, they are respectively:

30 ℃ → 25 ℃/min → 250 ℃ of A temperature programme

30 ℃ → 15 ℃/min → 250 ℃ of B temperature programme

30 ℃ → 5 ℃/min → 250 ℃ of c program intensification

(1) selecting methyl alcohol, heptane, isoamyl acetate is testing compound, on HP-5 post, measure its retention time under 250 ℃, 200 ℃, 150 ℃, 100 ℃, 50 ℃ and 30 ℃ of six constant temperature, methyl alcohol is respectively in corresponding temperature point retention time: 1.988min, 2.141min, 2.338min, 2.596min, 3.012min, 3.346min; Heptane is respectively in corresponding temperature point retention time: 2.011min, 2.189min, 2.458min, 2.999min, 5.171min, 8.427min; Isoamyl acetate is respectively in corresponding temperature point retention time: 2.036min, 2.241min, 2.623min, 3.904min, 13.501min, 34.415min.

(2) get virtual dead time τ=1.85min, according to formula 13, calculate respectively methyl alcohol, heptane, isoamyl acetate in the capacity factor measure under 250 ℃, 200 ℃, 150 ℃, 100 ℃, 50 ℃ and 30 ℃ of six constant temperature and get natural logarithm.Methyl alcohol is respectively in the natural logarithm of corresponding temperature point capacity factor measure :-2.614 ,-1.859 ,-1.338 ,-0.912 ,-0.468 ,-0.215; Heptane is respectively in the natural logarithm of corresponding temperature point capacity factor measure :-2.454 ,-1.703 ,-1.118 ,-0.479,0.583,1.267; Isoamyl acetate is respectively in the natural logarithm of corresponding temperature point capacity factor measure :-2.308 ,-1.561 ,-0.876,0.102,1.839,2.867.

(3) make respectively the lnk of methyl alcohol, heptane, isoamyl acetate with the scatter diagram of temperature T variation, see Fig. 2, Fig. 3, Fig. 4.Fig. 2 is the scatter diagram that the lnk of methyl alcohol changes with temperature T, selects capacity factor measure data point 1 at 30 ℃ as low temperature data point (lnk _a, T _a), choose capacity factor measure data point 3 at 100 ℃ as intermediate point (lnk _b, T _b), the capacity factor measure data point 4 at 150 ℃ is as high-temperature data point (lnk _c, T _c), 3 data points therefore selecting are respectively (0.215,30 ℃), (0.912,100 ℃) and (1.338,150 ℃); Fig. 3 is the scatter diagram that the lnk of heptane changes with temperature T, selects capacity factor measure data point 1 at 30 ℃ as low temperature data point (lnk _a, T _a), the capacity factor measure data point 3 at 100 ℃ is as intermediate point (lnk _b, T _b), the capacity factor measure data point 4 at 150 ℃ is as high-temperature data point (lnk _c, T _c), 3 data points therefore selecting are respectively respectively (1.267,30 ℃), (0.479,100 ℃) and (1.118,150 ℃); Fig. 4 is the scatter diagram that the lnk of isoamyl acetate changes with temperature T, by 6 somes numberings, selects capacity factor measure data point 1 at 30 ℃ as low temperature data point (lnk _a, T _a), the capacity factor measure data point 3 at 100 ℃ is as intermediate point (lnk _b, T _b), the capacity factor measure data point 5 at 200 ℃ is as high-temperature data point (lnk _c, T _c), 3 data points therefore selecting are respectively respectively (2.867,30 ℃), (0.102,100 ℃) and (1.561,200 ℃).

(4) according to formula 12, obtain respectively the parameter lambda of methyl alcohol, heptane, isoamyl acetate, be respectively methyl alcohol: λ=8.079;

Heptane: λ=3.617; Isoamyl acetate: λ=4.785.

(5) parameter lambda of obtaining in step (4) is updated in formula 10, sets up the retention equation of compound retention factors and temperature relation in Temperature Programmed Processes, be respectively:

Methyl alcohol: lnk=8.2063/ (1.0000+0.0014T)-8.0788

Heptane: lnk=6.4137/ (1.0000+0.0104T)-3.6166

Isoamyl acetate: lnk=10.1003/ (1.0000+0.0107T)-4.7846

(6) in computer program, input column's length L, chromatographic column column internal diameter d _c, mobile phase chromatographic column entrance with compare temperature under β, testing compound initial concentration, six constant temperature and corresponding retention time, virtual dead time, retention equation, the initial temperature of single-order temperature programme, the temperature of termination, heating rate, initial temperature with pressure P i, Po, mobile phase viscosities il, the post of outlet under time of keeping under time of keeping and intensification final temperature, can calculate their retention times under each temperature programme.

(7) on HP-5 post, measure the experiment value t of methyl alcohol, heptane, isoamyl acetate retention time under above three single-order temperature programme conditions _exp, and with prediction and calculation value t _calrelatively, according to formula 25, calculate Relative Error RE:

RE%=(t _cal-t _exp)/t _{r, exp}* 100 formulas 25

The results are shown in Table one:

The virtual dead time is while being 1.85min, methyl alcohol, heptane and isoamyl acetate retention time experiment value, predicted value and the relative error under three temperature programmes

Embodiment 2

The process of the present embodiment and condition are identical with embodiment 1, different:

(1) virtual dead time τ is 1.40min;

(2) according to formula 13, calculate respectively capacity factor measure under 250 ℃, 200 ℃, 150 ℃, 100 ℃, 50 ℃ and 30 ℃ of six constant temperature of methyl alcohol, heptane, isoamyl acetate and get natural logarithm.Methyl alcohol is respectively in the natural logarithm of corresponding temperature point capacity factor measure :-0.868 ,-0.637 ,-0.401 ,-0.157,0.141,0.329; Heptane is respectively in the natural logarithm of corresponding temperature point capacity factor measure :-0.829 ,-0.573 ,-0.281,0.133,0.991,1.613; Isoamyl acetate is respectively in the natural logarithm of corresponding temperature point capacity factor measure :-0.789 ,-0.510 ,-0.135,0.581,2.157,3.160.

(3) make respectively the lnk of methyl alcohol, heptane, isoamyl acetate with the scatter diagram of temperature T variation.3 data point (lnk that methyl alcohol is selected _a, T _a), (lnk _b, T _b) and (lnk _c, T _c) be respectively (0.329,30 ℃), (0.157,100 ℃) and (0.401,150 ℃); 3 data points that heptane is selected are respectively (1.613,30 ℃), (0.133,100 ℃) and (0.281,150 ℃); 3 data points that isoamyl acetate is selected are respectively (3.160,30 ℃), (0.581,100 ℃) and (0.510,200 ℃).

(4) according to formula 12, obtain respectively the parameter lambda of methyl alcohol, heptane, isoamyl acetate, be respectively methyl alcohol: 2.108;

Heptane: 1.495; Isoamyl acetate: 2.055.According to formula 10, set up compound in Temperature Programmed Processes, the retention equation of retention factors and temperature relation, is respectively:

Methyl alcohol: lnk=2.7292/ (1.0000+0.0040T)-2.1080

Heptane: lnk=5.0945/ (1.0000+0.0213T)-1.4947

Isoamyl acetate: lnk=8.9814/ (1.0000+0.0241T)-2.0552

The results are shown in Table two:

The virtual dead time is while being 1.40min, methyl alcohol, heptane and isoamyl acetate retention time experiment value, predicted value and the relative error under three temperature programmes

Embodiment 3

The process of the present embodiment and condition are identical with embodiment 1, different:

(1) virtual dead time τ is 0.90min;

(2) according to formula 13, calculate respectively capacity factor measure under 250 ℃, 200 ℃, 150 ℃, 100 ℃, 50 ℃ and 30 ℃ of six constant temperature of methyl alcohol, heptane, isoamyl acetate and get natural logarithm, methyl alcohol is respectively in the natural logarithm of corresponding temperature point capacity factor measure: 0.189,0.321,0.468,0.634,0.853,1.000; Heptane is respectively in the natural logarithm of corresponding temperature point capacity factor measure: 0.211,0.359,0.548,0.847,1.557,2.124; Isoamyl acetate is respectively in the natural logarithm of corresponding temperature point capacity factor measure: 0.233,0.398,0.649,1.205,2.639,3.617.

(3) make respectively the lnk of methyl alcohol, heptane, isoamyl acetate with the scatter diagram of temperature T variation.3 data point (lnk that methyl alcohol is selected _a, T _a), (lnk _b, T _b) and (lnk _c, T _c) be respectively: (1.000,30 ℃), (0.634,100 ℃) and (0.468,150 ℃); 3 data points that heptane is selected are respectively (2.124,30 ℃), (0.847,100) and (0.548,150 ℃); 3 data points that isoamyl acetate is selected are respectively (3.617,30 ℃), (1.205,100 ℃) and (0.398,200 ℃).

(4) according to formula 12, obtain respectively the parameter lambda of methyl alcohol, heptane, isoamyl acetate, be respectively methyl alcohol: 0.446; Heptane: 0.216; Isoamyl acetate: 0.586.According to formula 10, set up compound in Temperature Programmed Processes, the retention equation of retention factors and temperature relation, is respectively:

Methyl alcohol: lnk=1.6913/ (1.0000+0.0057T)-0.4455

Heptane: lnk=4.8248/ (1.0000+0.0354T)-0.2163

Isoamyl acetate: lnk=9.9436/ (1.0000+0.0455T)-0.5855

The results are shown in Table three:

The virtual dead time is while being 0.90min, methyl alcohol, heptane and isoamyl acetate retention time experiment value, predicted value and the relative error under three temperature programmes

Claims (1)

1. the method based on polymer crystallization behavior derivation retention equation predictor intensification retention time, the method is for HP6890 gas chromatograph and nonpolar HP-5 chromatographic column, with described polymer crystallization behavior derivation retention equation, predict gas chromatography retention time, it is characterized in that comprising following process:

The first step, the retention equation curve of deriving and containing temperature, capacity factor measure based on polymer crystallization behavior:

(1) according to the crystallinity of high molecular polymer and the linear variation relation of density, during the complete crystallization of superpolymer, density is maximum, and its density is ρ _c, crystallinity

and complete when non-crystallizable density minimum, its density is ρ _a, crystallinity

in the density of other crystalline states between minimum and maximum; The crystallinity formula of superpolymer is by point (ρ _a, 0%) and point (ρ _c, 100%) just can determine, as shown in Equation 1:

formula 1

In formula 1: for the crystallinity of superpolymer, ρ is corresponding density, ρ _cdensity during for the complete crystallization of superpolymer,

ρ _afor complete density when non-crystallizable of superpolymer, and there is the 0< of relation ρ _a≤ ρ≤ρ _c;

By formula 1, can be obtained

as shown in Equation 2:

formula 2

(2), because compound is in HP-5 chromatographic column, capacity factor measure variation with temperature non-rectilinear relation, but the concave curve relation of monotone decreasing, for linear formula 2 is become to curve, need to be multiplied by ρ to formula 2 equation right-hand members _cbe out of shape with the coefficient that is compared to of ρ, become formula 3:

formula 3

Formula 3 is carried out to differentiate, and first order derivative is greater than 0, second derivative is less than 0, and formula 3 is monotonically increasing convex curve; Arrangement formula 3 obtains formula 4:

formula 4

For formula 4 being become to the concave curve of monotone decreasing, introduce parameter x, and order

substitution formula 4 obtains formula 5:

formula 5

The function that formula 5 is constructed is through (ρ _a, 1) and (ρ _c, 0) and two end points, and field of definition ρ >0; Formula 5 is carried out to differentiate, and first order derivative is less than 0, second derivative is greater than 0, the concave curve that formula 5 is monotone decreasing; Formula 5 is converted to deriving 6:

$\mathrm{\&rho;}=\frac{{\mathrm{\&rho;}}_a\&CenterDot;{\mathrm{\&rho;}}_c}{{\mathrm{\&rho;}}_a+({\mathrm{\&rho;}}_c-{\mathrm{\&rho;}}_a)\&CenterDot;x}$ Formula 6

(3) in order to utilize the retention time of the crystallinity behavior prediction gas chromatography of superpolymer, the x in formula 6, ρ need to be connected with the natural logarithm lnk of temperature T, capacity factor measure respectively, be built into retention equation; Making x is the monotonically increasing linear function of T, and through (T _a, 0) and (T _c, 1) and two point, wherein T _a<T _c, according to 2 straight line formulas, there is formula 7:

$x=\frac{1}{T_c-T_a}(T-T_a)$ Formula 7

In formula 7: T _aand T _cfor known temperature, by experiment, determined, and regulation T _a<T _c;

T is unknown temperatures;

Make ρ=lnk, ρ _a=lnk _c, ρ _c=lnk _a, and formula 7 is updated in formula 6, there is formula 8:

$\ln k=\frac{{\ln k}_a\&CenterDot;{\ln k}_c}{{\ln k}_c+({\ln k}_a-{\ln k}_c)\&CenterDot;\frac{T-T_a}{T_c-T_a}}$ Formula 8

In formula 8: T _aand T _cfor known temperature, by experiment, determined, and regulation T _a<T _c;

Lnk _aand lnk _cbe respectively compound at corresponding temperature T _aand T _cunder the natural logarithm of capacity factor measure,

By experiment, determined, and set lnk _c<lnk _a;

T is unknown temperatures, and lnk is the natural logarithm of the capacity factor measure of compound under corresponding temperature T;

Formula 8 is through point (lnk _a, T _a) and point (lnk _c, T _c) the monotone decreasing concave curve of lnk to T, wherein the span of lnk is to be greater than 0 positive number; But due in gas chromatography, the lnk of compound can just can bear, therefore by lnk, lnk _aand lnk _call add non-negative parameter lambda, guarantee lnk+ λ, lnka+ λ and lnk _c+ λ value is positive number, can obtain formula 9 by formula 8:

$\ln k+\mathrm{\&lambda;}=\frac{({\ln k}_a+\mathrm{\&lambda;})\&CenterDot;({\ln k}_c+\mathrm{\&lambda;})}{({\ln k}_c+\mathrm{\&lambda;})+[({\ln k}_a+\mathrm{\&lambda;})-({\ln k}_c+\mathrm{\&lambda;})]\&CenterDot;\frac{T-T_a}{T_c-T_a}}$ Formula 9

Arrangement formula 9 obtains formula 10 and formula 11:

$\ln k=\frac{({\ln k}_a+\mathrm{\&lambda;})\&CenterDot;({\ln k}_a+\mathrm{\&lambda;})}{({\ln k}_c+\mathrm{\&lambda;})+({\ln k}_a-{\ln k}_c)\&CenterDot;\frac{T-T_a}{T_c-T_a}}-\mathrm{\&lambda;}$ Formula 10

$\mathrm{\&lambda;}=\frac{{\ln k}_c\&CenterDot;(\ln k-{\ln k}_a)+\ln k\&CenterDot;({\ln k}_a-{\ln k}_c)\&CenterDot;\frac{T-T_a}{T_c-T_a}}{({\ln k}_a-\ln k)-({\ln k}_a-{\ln k}_c)\&CenterDot;\frac{T-T_a}{T_c-T_a}}$ Formula 11

In order to determine non-negative parameter lambda, except (lnk _a, T _a) and (lnk _c, T _c) outside 2, between 2 o'clock, increase known data point (lnk _b, T _b), by formula 11, obtain formula 12, utilize formula 12 just to obtain parameter lambda:

$\mathrm{\&lambda;}=\frac{{\ln k}_c\&CenterDot;({\ln k}_b-{\ln k}_a)+{\ln k}_b\&CenterDot;({\ln k}_a-{\ln k}_c)\&CenterDot;\frac{T_b-T_a}{T_c-T_a}}{({\ln k}_a-{\ln k}_b)-({\ln k}_a-{\ln k}_c)\&CenterDot;\frac{T_b-T_a}{T_c-T_a}}$ Formula 12

Thus, only utilize 3 known data point (lnk _a, T _a), (lnk _b, T _b) and (lnk _c, T _c) obtain λ, then λ substitution formula 10 just can be determined to retention equation, predict gas chromatography retention time; Point (lnk wherein _a, T _a) and point (lnk _c, T _c) for determining two end points of retention equation, and point (lnk _b, T _b) for determining the concavo-convex degree of retention equation curve;

Second step, the virtual dead time of setting chromatographic column arbitrary temp point:

Chromatographic column design temperature variation range is 30-250 ℃, measures compound at T ₁=30 ℃, T ₂=50 ℃, T ₃=100 ℃, T ₄=150 ℃, T ₅=200 ℃ and T ₆retention time under=250 ℃ of six constant temperature is respectively t _r1, t _r2, t _r3, t _r4, t _r5and t _r6, determine wherein minimum retention time value, to be less than any one time value of this minimum value, all can be used as virtual dead time τ;

The 3rd step, deterministic compound is in any capacity factor measure of temperature spot:

(1) according to the retention time t under measure in second step six constant temperature _r1, t _r2, t _r3, t _r4, t _r5, t _r6the virtual dead time τ having determined, employing formula 13, calculates retention factors corresponding under six constant temperature and is respectively k ₁, k ₂, k ₃, k ₄, k ₅and k ₆:

K=(t _r-τ)/τ formula 13

In formula 13: the capacity factor measure that k is compound,

τ is the virtual dead time,

T _rretention time for corresponding each temperature spot;

(2) capacity factor measure of the compound calculating in step (1) is got to natural logarithm lnk, make lnk ₁, lnk ₂, lnk ₃, lnk ₄, lnk ₅, lnk ₆with temperature T ₁, T ₂, T ₃, T ₄, T ₅, T ₆the scatter diagram changing, according to the concavo-convex distribution situation of 6 data points, therefrom selects 3 data point (lnk _a, T _a), (lnk _b, T _b) and (lnk _c, T _c), according to formula 12, obtain parameter lambda, according to formula 10, set up retention equation, thereby can deterministic compound in the capacity factor measure of temperature spot arbitrarily;

The 4th step, the temperature value of any time of determining chromatographic column in Temperature Programmed Processes:

(1) the T.T. t that determine procedures heats up and needs _total:

The T.T. t that heats up and need with formula 14 determine procedures while adopting single-order temperature programme _total:

T _total=t _h1+ t+t _h2formula 14

In formula 14: t _h1for the retention time of initial temperature, empirical value is: 1-5min;

T _h2for the retention time of the final temperature of single-order temperature programme;

T be single-order temperature programme need the time, by formula 15, calculated:

T=(T _f-T _o)/r formula 15

In formula 15: T _oinitial temperature for single-order temperature programme;

T _ffinal temperature for single-order temperature programme;

R is the heating rate of single-order temperature programme, and the experience span of r is 5-30 ℃/min;

(2) determine that mobile phase flows through the time t of whole chromatogram experience _i:

The virtual dead time τ differential of setting is become to m equal portions, and every equal portions are △ τ:

$\mathrm{\&tau;}=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;\&tau;}$ Formula 16

In formula 16: τ is the virtual dead time, by the 3rd step, determined;

M is the umber that waits in the time interval, and it is enough large that setting value is wanted;

△ τ is the time of every equal portions, by waiting umber m to determine;

By formula 17, determined the distance △ l that in the time △ τ of every equal portions, mobile phase is passed by:

Δ l=u Δ τ formula 17

In formula 17: u is column performance, is determined by formula 18:

$u=\frac{3}{32L\&CenterDot;\mathrm{\&eta;}}\&CenterDot;\frac{{d_c}^2}{4}\&CenterDot;\frac{{({P_i}^2-{P_o}^2)}^2}{({P_i}^3-{P_o}^3)}$ Formula 18

In formula 18: L is column length, is determined by actual measurement;

D _cfor chromatographic column internal diameter, by actual measurement, determined;

Pi be mobile phase at the pressure of chromatographic column porch, by actual measurement, determined;

Po be mobile phase at the pressure in chromatographic column exit, by actual measurement, determined;

η is mobile phase viscosity, by actual measurement, is determined;

The distance △ l that in the time △ τ of every equal portions, mobile phase is passed by is carried out to integration, and the distance that mobile phase is passed by equals column length L:

$L=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;l}$ Formula 19

In formula 19: L is column length, is determined by actual measurement;

△ l is the distance △ l that the interior mobile phase of the time △ τ of every equal portions is passed by, and by formula 17, is determined;

N is the distance equal portions sum that whole root chromatogram column contains;

Mobile phase is gone to the time t that time of i equal portions experiences _i:

T _i=i △ τ formula 20

In formula 20: t _ifor mobile phase flows to the time that time of i equal portions experiences;

I is the umbers such as time;

△ τ is the time of every equal portions, by formula 16, is determined;

(3) when deterministic compound flows to the time of i equal portions with mobile phase, the temperature T that chromatographic column is corresponding _i:

Work as t _i<t _h1, chromatographic column temperature T _i=T _o;

Work as t _h1<t _i< t _h1+ t), chromatographic column temperature Ti=r * (t _i-t _h1)+T _o;

As (t _h1+ t)≤t _i≤ (t _h1+ t+t _h2), chromatographic column temperature T _i=T _f;

The 5th step, predict the retention time of component to be measured:

By definite T in the 4th step _iin substitution formula 10, when calculating compound and flowing to the time of i equal portions with mobile phase, namely flow to i equal portions apart from time, corresponding capacity factor measure k _i;

(1) utilize mobile phase flow to i equal portions apart from time Retention factor k corresponding to compound _i, according to formula 21 and 22, calculate respectively testing compound with mobile phase flow to i equal portions apart from time fixing mutually and the concentration of mobile phase:

K _i* β=C _sni/ C _mniformula 21

C _mni+ C _sni=C _niformula 22

In formula 21: β is chromatographic column self compare numerical value,

C _mniand C _snibe respectively mobile phase flow to i equal portions apart from time, testing compound is at n

Mobile phase and fixing concentration in mutually in equal portions distances;

In formula 22: C _nifor mobile phase flow to i equal portions apart from time, the total concentration of testing compound in n equal portions distance, it is determined by formula 23 and formula 24:

C _ni=C _{s (n-1) i}+ C _{m (n-1) (i-1)}formula 23

C _m00=1 μ g/ml formula 24

In formula 23 and formula 24:

C _m00for the concentration of the initial sample introduction of component,

C _{s (n-1) i}for mobile phase flow to i equal portions apart from time, compound is in the fixing phase of n equal portions distance

In concentration;

C _{m (n-1) (i-1)}for mobile phase flow to i-1 equal portions apart from time, compound is n-1 equal portions distance

Mobile phase in concentration;

(2) determining of testing compound retention time:

According to (1) of the 5th step, by computing machine calculate obtain mobile phase flow to i-1, i and i+1 equal portions apart from time, last equal portions distance of chromatographic column N equal portions apart from, testing compound is respectively C in the concentration of mobile phase _{mN (i-1)}, C _mNiand C _{mN (i+1)}, three concentration are compared:

Work as C _{mN (i-1)}<C _mMi>C _{mN (i+1)}time, stop calculating, while being i by formula 20 calculating equal portions apart from number, the time t needing altogether _i, this time is retention time;

When not meeting above-mentioned inequality C _{mN (i-1)}<C _mNi>C _{mN (i+l)}time, continue to repeat above-mentioned calculating, until reach, meet inequality C _{mN (i-1)}<C _mNi>C _{mN (i+1)}till, determine retention time.

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