Chapter 2 Gas Chromatography(GC)

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1 Chapter 2 Gas Chromatography(GC)
§2-1 Summary ●Chromatographic separation technique(色谱分离）: A separation technique based on partition of 2 or more substances in a mixture in two phases(色谱法、色层法、层析法,chromatographer） ● Chromatographic analysis（色谱分析）: Chromatographic separation applied on analytical chemistry Advantages: High separation efficiency, high detection efficiency, fast analytical velocity

2 GC ●Mobile phase & Stationary phase（流动相与固定相): Chromatographic separation involving partition of different species in a mixture in two phases, among which one phase (solid or liquid) does not move (stationary phase) , the other phase (gas or liquid) takes the sample mixture to pass through the stationary phase packed in the column( mobile phase) Separations are affected due to the differences of substances’ affinities for a mobile phase and a stationary phase(分离原理）.

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4 GC To waste Flow meter Detector Flow controller Oven Gas supply Column
(In one of these positions) Injection system Amplifier Integrator Recorder

5 Setup of Gas Chromatograph
GC 皂膜流量计 转字流量计 调整仪，标准仪 Setup of Gas Chromatograph

6 inert gases wothout interaction with analytes or stationary phase
管状的 , IR, FPD Thermal conductivity detector Flame photometric detector Hydrogen flame ionization detector Electron capture detector

7 Chromatogram of xylene isomers on a polar column
GC Chromatogram of xylene isomers on a polar column

8 Y

9 Chromatogram GC s t Rotention time t' 2 Dead 0.607h time Y h Air peak
12 4 Peak width at a half height Peak width at peak base Adjusted retention time Rotention time Dead time Air peak 0.607h 1/2 h 2 s Y t' R t M Injection Response signal Chromatogram Time(arbitrary units)

10 Nomenclature of Chromatographic separation
●Chromatographic Curve & Chromatogram The chart of output detector response (concentration) versus time The protuberance in the curve is called chromatographic peak 如果进样量很小，浓度很低，在吸附等温线（气固吸附色谱）或分配等温线（气液分配色谱）的线性范围内，则色谱峰是对称的。

11 Nomenclature of Chromatographic separation
●Baseline(基线) Chromatographic curve under the experimental operation conditions, no components of materials flow out after the column(在实验操作条件下，色谱柱后没有样品组分流出时的流出曲线称为基线，反映检测器系统噪声（Noise) 随时间的变化情况。稳定的基线应该是一条水平直线。) ●Baseline drift(基线漂移）refer to 基线随时间定向的缓慢变化 ●Peak height refer to Vertical distance from the vertex of chromatographic peak to baseline 色谱峰顶点与基线之间的垂直距离，以（h）表示。

12 Nomenclature of Chromatographic separation
信号 进样 空气峰 色谱峰 h a 色谱流出曲线 ▲Chromatogram and chromatographic peak ▲ Baseline（a） ▲ Peak height（h）

13 Nomenclature of Chromatographic separation
●Retention value 表示试样中各组分在色谱柱中滞留时间的数值。通常用时间或用将组分带出色谱柱所需载气的体积来表示。 ■ Rely on component partition on two phases (or absorption) ■Thermodynamic controlled (Properties of stationary phase & operation conditions) ■ Qualitative Base ● Dead Time tM 不被固定相吸附或溶解的物质(如空气，甲烷等）进入色谱柱时，从进样到出现峰极大值（浓度）所需的时间称为死时间，它正比于色谱柱的空隙体积。见图

14 Nomenclature of Chromatographic separation
因为这种物质不被固定相吸附或溶解，故其流动速度将与流动相流动速度相近。测定流动相平均线速ū时，可用柱长L与tM的比值计算，即 ū = L/tM ●Rotention time tR The time at which the maximum of the peak appears after sample injection 见图

15 Nomenclature of Chromatographic separation
●Adjusted rotention time(tR´) The difference between the rotention time and dead time 某组分的保留时间扣除死时间后，称为该组分的调整保留时间，即 tR´= tR  tM More time the component spends due to dissolution in (or adsorption on) the stationary phase than inert components without interaction. 保留时间是色谱法定性的基本依据，但同一组分的保留时间常受到流动相流速的影响，因此色谱工作者有时用保留体积来表示保留值。

16 Nomenclature of Chromatographic separation
●Dead Volume VM 指色谱柱在填充后，柱管内固定相颗粒间所剩留的空间、色谱仪中管路和连接头间的空间以及检测器的空间的总和。当后两相很小可忽略不计时，死体积可由死时间与色谱柱出口的载气流速F0（cm3·min-1）计算。 VM = tMF0 式中 F0为扣除饱和水蒸气压并经温度校正的流速。 仅适用于气相色谱，不适用于液相色谱

17 Nomenclature of Chromatographic separation
●Rotention volume VR 指从进样开始到被测组分在柱后出现浓度极大点时所通过的流动相的体积。保留时间与保留体积关系： VR= tR F0 = tM F0 ●Adjusted rotention volume VR 某组分的保留体积扣除死体积后，称为该组分的调整保留体积。 VR = VR  VM = tR F0 VR， VR’ do not depend on velocity of the carrier gas.

18 Nomenclature of Chromatographic separation
●Relative rotention value r21 The ratio of adjusted rotention value of the second component to that of the first component r21= tR(2)  / tR(1)´= VR(2) / VR(1)  tR(2) / tR(1) VR(2) / VR(1) 由于相对保留值只与柱温及固定相性质有关，而与柱径、柱长、填充情况及流动相流速无关，因此，它在色谱法中，特别是在气相色谱法中，广泛用作定性的依据。 ■The higher r21 , the bigger difference between the adjusted rotention values of adjacent components , the better the separation. When r21=1, the two components can not separate at all.

19 Nomenclature of Chromatographic separation
在定性分析中，通常固定一个色谱峰作为标准（s），然后再求其它峰（i）对这个峰的相对保留值，此时可用符号表示，即  = tR (i) / tR  (s) 式中tR (i)为后出峰的调整保留时间，所以总是大于1的。相对保留值往往可作为衡量固定相选择性的指标，又称选择因子。 ● Peak width(区域宽度) 色谱峰的区域宽度是色谱流出曲线的重要参数之一，用于衡量柱效率及反映色谱操作条件的动力学因素。表示色谱峰区域宽度通常有三种方法。

20 Nomenclature of Chromatographic separation
● Standard deviation  Half –width of chromatographic peak at times peak height (0.607倍峰高处色谱峰宽的一半) ●Peak width at half-height(半峰宽度、半峰宽、区域宽度）Y1/2 即峰高一半处对应的峰宽。它与标准偏差的关系为 Y1/2=2s SQR(2ln2)=2.354 ●Peak width at peak base(峰底宽度) Y 即色谱峰两侧拐点上的切线在基线上的截距。它与标准偏差的关系是 Y = 4  Due to easiness to measure, Y1/2 is always used to denote peak width.

21 Nomenclature of Chromatographic separation
从色谱流出曲线中，可以得到许多重要信息： ●Judge the number of the components included a mixture based on the number of peaks ●Qualitative analysis based on the rotention value of chromatographic peak ●Quantitative analysis based on areas or heights of chromatographic peaks ●Rotention value and peak width of chromatographic peaks is the basic to evaluate separation efficiency of chromatographic column ●色谱峰两峰间的距离，是评价固定相（或流动相）选择是否合适的依据。

22 §2.2 Theoretical foundation of gas chromatographic analysis
2.2.1Gas solid or Gas liquid chromatography Capillary column（毛细管柱）: The column has internal diameter of less than one mm, and inner wall of the column is usually coated with a film of stationary liquid Chromatographic column Packed column(填充柱）: Packed stationary usually made from metal materials (copper or stainless steel) or glass, with a height of m and inside diameter of 2-6mm. U-shape or screwy(螺旋形） Stationary phase Gas-solid chromatography（气-固色谱）: porous solid materials or adsorptive particles with higher surface area Mechanism: Adsorption & Elution (desorption) Gas-liquid chromatography（气-液色谱）: Chemical inert solid particles(担体, support) coated with a film of organic chemical of high-boiling point（Stationary liquid,固定液） Mechanism: Dissolution & volatilization

23 §2.2 Theoretical foundation of gas chromatographic analysis
Partition Process: Adsorption, elution, and dissolution, volatilization process of the substances between stationary phase and mobile phase. Partition Coefficient(K): Concentration ratio of the component in stationary phase and mobile phase when the partition process arrives at equilibrium under given temperature. K = Concentration of the component in stationary phase Concentration of the component in mobile phase = cS/cM Gas chromatographic analysis based on the difference of the partition coefficients of different substances

24 §2.2 Theoretical foundation of gas chromatographic analysis
Partition ratio (capacity factor, capacity ratio, k): Mass ratio of the component in two phases when partition process arrives at equilibrium under given temperature and pressure k = mS / mM mS refers to mass of the component distributed in stationary phase, mS mass of the component distributed in mobile phase Relationship between k and K K = cS/cM= (mS/VS) / (mM / VM) =k VM/ VS = kb

25 VM refers to mobile phase volume in column, that is,柱内固定相颗粒间的空隙 (lacuna）体积 。
VS Stationary phase volume in column (在气-液色谱中为固定液体积，气-固色谱中为吸附剂的表面容量。 Phase ratio(相比，b): VM / VS, 反映各种色谱柱柱型及其结构特征 Packing column: 6-35, Capillary column:

26 Stationary phase Stationary liquid Capillary wall

27 Relationship of K and k ● K refers to concentration ratio and k mass ratio K and k depends on thermodynamic properties of the components and stationary phase, Tc(柱温），Pc(柱压） ● K only relys on properties of the component and double phases, but not phase ratio. But k relys on not only properties of the component and double phases, but also phase ratio( amount of stationary phase) ● With a given chromatographic system, separation of the components is determined by relative amount of the components in both phases, but not relative concentration. The bigger k value, the longer rotention time, the easier separation. k =0 corresponds to dead time tM.

28 Rs = uS/u = w = mM / (mS + mM) =1/(1+mS / mM) = 1/(1+k)
●Retardation factor(滞留因子, Rs）： Ratio of the velocity of carrier gas and the component in column: Rs = uS/u = w = mM / (mS + mM) =1/(1+mS / mM) = 1/(1+k) Where u refers to velocity of carrier gas in column in unit of cm.s-1, u velocity of the component in column, w mass fraction.

29 tR = L /uS = tMu /uS = tM u / uS = tM(1+k)
Defining L as column length, following formula are vivid: tR = L / uS tM = L / u tR = L /uS = tMu /uS = tM u / uS = tM(1+k) k = (tR-tM) / tM = t’R / tM Above equation can be employed to evaluate k value.

30 2.2.1Basic theory of chromatographic separation
●Partition of different components in double phases Depending on partition coefficient, molecular structure and properties of the components, stationary phase, mobile phase. Characterized by rotention value (rotention time or rotention volume), thermodynamic controlled. ●Movement of different components in column Depending on mass transfer(传质) resistance of different components in stationary phase and mobile phase. Characterized by peak width at half-height, kinetic controlled

31 Theories Two approaches can be taken to explain the separation process
Plate theory – proposed in 1941 by Martin and Synge. Based on an analogy with distillation and counter current extraction Rate theory – accounts for the dynamics of a separation – 1956, J. J. Van Deemter. Each has advantages and limitations.

32 ●Plate theory(塔板理论) 借用传统的蒸馏过程处理色谱过程
将色谱柱比作一个分馏塔，色谱柱由许多假想的塔板组成（即将色谱柱分成许多各小段），在每一个塔板内，一部分空间被涂在担体上的液相占据，另一部分空间则充满气相（载气），载气占据空间称为板体积DV.当欲分离的组分随载气进入色谱柱后，就在两相间进行分配。由于流动相在不停地移动，组分就在这些塔板间隔的气液两相间不断地达到分配平衡。

33 Plate theory assumes: ●在一小段间隔（塔板）内，气相平均组成与液相平均组成能很快达到分配平衡。达到分配平衡的一小段柱长称为理论塔板高度H（Height equivalent to theoretical plate) ●载气进入色谱柱，不是连续的，而是脉动式的，每次进气为一个板体积 ●试样开始时都加在第0号塔板上，且试样沿色谱柱方向的扩散（纵向扩散）可忽略不计 ●分配系数在各塔板上是常数

34 Assuming the column consists of 5 plates, n=5 (number of theoretical plates), r is defined as number of plate, r= 0,1, 2, …, n-1. With m=1, k=1, w=1/2, when carrier gas of one more plate volume enters the column pulsantly, partition in each plate is shown as follows: Mass in mobile phase Mass in stationary phase 原塔板1固定相中组分的质量（ =0.25)与随载气带入的原塔板0流动相中组分质量(0.125)重新分配:( )/2=0.188

35 Total amount of the solute in a plate
Partition table of the component in any plate in a column with n=5, k=1 and w=1/2 Total amount of the solute in a plate

36 Chromatogram of the component in a column with n=5, N is number of plate volume of carrier gas
● Peak asymmetry since n is too small ● Concentration maximum at N= 8-9 ● Peak symmetry near normal distribution when n > 50 ● n=103 ~ 106 for gas chromatography

37 When number of theoretical plates is big enough, chromatogram approaches normal distribution curve, following relationship between concentration C and time t is obtained: 流出曲线方程式 Where C0 is injection concentration(进样浓度）, C concentration at outlet（出口） of the column at time t

38 Relationship of n to peak width:
Where L is length of chromatographic column, tR, Y1/2, Y in the same units, n theoretical plate number, H theoretical plate height.

39 为了扣除死时间或死体积的影响，实际工作中常用有效塔板数（Effective plate number) 和有效塔板高度（Effective plate height)作为柱效能指标：
1+k k 2 • n有效

40 ●色谱柱的柱效能还与物质的性质有关，同一色谱柱的柱性能对不同物质是不同的。
●色谱柱的理论塔板数越大，表示组分在色谱柱中达到分配平 衡的次数越多，固定相的作用越显著，因而对分离越有利。但不 能预言并确定各组分是否有被分离的可能，因为分离的可能性决定于试样混合物在固定相中分配系数的差别，而不决定于分配 次数的多少。 ●n有效不能作为有无实现分离可能的依据，而只是在一定条件下柱分离能力发挥程度的标志。 ●塔板理论没有考虑动力学因素的影响，因而不能解决塔板高度受什么因素影响以及流速对理论塔板数的影响等问题。

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42 （扩散）

43 Rate theory of chromatography
It is based on a Gaussian distribution similar to that of plate theory He was attempting to account for the dynamics of the separation process.

44 B H = A + +Cu u 0.01k2 dp2 2 + (1+k)2 Dg 3 （填充的不均匀性） （弯曲因子） （固定相的液膜厚度）
（组分在载气流中的分子扩散系数） （固定相的液膜厚度）

45 (涡流扩散项） （分子扩散项） （液相传质过程） 0.01k2 dp2 (1+k)2 Dg u Gas term(气相传质过程）

46 (涡流扩散项） （分子扩散项） （传质项）

47 涡流扩散项（vortex diffusion term)
●由于填充物颗粒的阻碍作用，当气体通过时，会不 断改变流动方向，使样品组分在气相中形成类似“涡流”的流动，引起色谱峰的扩张。涡流扩散项的大小与填充物的平均颗粒直径dp(单位未cm)大小及填充的不均匀性有关，而与载气性质，线速度和组分无关。 ●使用细粒度和粒度分布均匀的颗粒作为担体，且填充均匀，可以减少涡流扩散，提高柱效能。 ●空心毛细管柱，涡流扩散项A为零。

48 返回

49 (Longitudinal diffusion term)
分子扩散项B/u(纵向扩散项) (Longitudinal diffusion term) 试样组分被载气带入色谱柱后，以“塞子”的形式存在于柱内很小一端空间中，在“塞子”的前后（纵向）存在着浓差而形成浓度梯度，使运动着的分子产生纵向扩散。纵向扩散项的大小B为： B=2gDg g 为弯曲因子，表示因载体填充在柱内而引起气体扩散路径弯曲的因素。Dg 为组分在气相中的扩散系数（cm2.s-1) B的影响因素： ● g 与填充物有关：由于固定相颗粒的存在，使分子不能自由扩散，从而使扩散程度降低。 ▲空心毛细管柱：没有填充物的阻碍，扩散程度最大，g = 1 ▲填充柱：由于填充物的阻碍，扩散路径弯曲，扩散程度降低，g<1. 对于硅藻土担体，g= 0.5 ~ 0.7.

50 ●纵向扩散项与组分在柱内的保留时间有关，保留时间越长（相当于载气流速越小），分子扩散项对色谱峰扩张的影响越显著。
●分子扩散项与组分在载气流中的分子扩散系数Dg 成正比。 ▲ Dg与组分及载气的性质有关： 相对分子质量越大，Dg越小 Dg 与载气密度的平方根或载气相对分子质量的平方根成反比。 Dg 也随柱温的升高而增加，但与柱压成反比。

51 返回

52 传质项C (Resistance to mass transfer)
包括气相传质阻力系数Cg 和液相传质阻力系数Cl

53 气相传质过程： 试样组分从气相移动到固定相表面的过程，在该过程中，试样组分将在两相间进行质量交换，即浓度分配。如气相传质过程速度慢，表示气相传质阻力大，便会引起色谱峰扩张。对于填充柱： Cg = 0.01k2•dp2 (1+k)2•Dg 上式中k为容量因子。dp 为填充物颗粒的平均直径。 Cg ∝ dp2 Cg ∝ 1/Dg 对于填充柱，固定相含量较高，在中等线速时，Cg 数值较小，通常可以忽略。

54 液相传质过程 试样组分从固定相的气液界面移动到液相内部，并发生质量交换，达到分配平衡，然后再返回气液界面的过程。在液相传质过程中，气相中的组分的其它分子仍然随载气不断地向柱口运动，从而造成峰形的扩张。 component molecule Stationary liquid support 液相传质阻力系数Cl Cl = 2 k df2 3(1+k)2Dl df refer to thickness of liquid member of stationary phase Dl diffusion coefficient of the component in liquid phase

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56 ▲ Enough big distance between chromatographic peaks of
§2-3 Selection and optimization of chromatographic separation conditions ●分离度（resolution) Whether a mixture can be separated or not depends on the difference of interaction (partition coefficient) between stationary phase and the various component molecules in the mixture and the operation conditions ▲Selecting appropriate stationary (possible separation,有分离可能性) ▲Selecting optimal operation condition (practical separation，实现可能性) 完全分离的依据 ▲ Enough big distance between chromatographic peaks of two components ▲ Enough thin peaks(见图）

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58 分离度R： The ratio of the difference of chromatographic rotention values of two adjacent components and half of sum of peak widths at peak base of two components(相邻两组分色谱峰保留值之差与两组分色谱峰峰底宽度总和之半的比值。分离度可以用来作为衡量色谱峰分离效能的指标。 ▲R越大，表明两组分分离效果越好 ▲保留值之差取决于固定液的热力学性质 ▲色谱峰宽窄反映色谱过程动力学因素，柱效能高低 对于峰形对称且满足正态分布的色谱峰： R=1, 分离程度为98%； R=1.5，分离程度可达99.7%. R=1.5， 可认为色谱峰已完全分开。

59 当两组分色谱峰分离较差，峰底宽度难以测量时，可用半峰宽度代替峰底宽度：
Basic equations to chromatographic separation (色谱分离基本方程式） 对于多组分混合物，在选择固定相实验操作条件时， 对于多组分混合物，在选择固定相及实验操作条件时，主要考虑难分离物质对。 由于其保留值差别很小，故可以认为Y1=Y2=Y, k1= k2 = k, eq(2-18) 可以变为： n1/ Y tR = •

60 1 4 n1/2 a -1 a k 1+k R = a 为选择因子 (*) 或： R = 1 4 n有效 1/2 a-1 a (**)
Base on above hypothesis, basic equation for chromatographic separation is defined as follows： 1 4 n1/2 a -1 a k 1+k R = a 为选择因子 (*) 或： R = 1 4 n有效 1/2 a-1 a (**) ▲分离度的影响因素

61 限制：L过长，保留时间延长，分析时间延长，色谱峰扩展。
■与柱效的关系（柱效因子） R ∝ n1/2 限制：L过长，保留时间延长，分析时间延长，色谱峰扩展。 增加柱长 使用性能优良的色谱柱，并选择最佳分离条件 减小塔板高度 ■与容量因子的关系 k值增大，有利于分离，但k > 10时，对R的增加不明显，也会显著增加分析时间 k的最佳范围：1 ~ 10

62 L = 16R2•H有效 a a-1 = n有效• H有效 ■与柱选择性的关系
■分离度、柱效、柱选择性的关系 L = 16R2•H有效 a a-1 2 = n有效• H有效 通过上式可以计算相关指标的值

63 例：设有一对物质，其a=1.15,要求在某填充柱上得到完全分离，试计算至少需要多长的色谱柱？
解：要实现完全分离，R≈1.5,故所需有效理论塔板数为： 使用普通色谱柱，一般有效理论塔板高度为0.1cm, 故所需柱长应为：

64 ●Selection of separation conditions (分离操作条件的选择)
▲Selection of carrier gas and its flow rate ▲Selection of column temperature(自学） ▲Properties and amount of mixed liquid（自学） ▲Properties and size of supports（自学） ▲Injection time and injection amount（自学）

65 ▲Selection of carrier gas and its flow rate
According to Van Deemter equation: Following equation can be obtained by differentiating above equation: and 实际工作中，为了缩短分析时间，常使流速稍高与最佳流速。

66 Combining above equation and Van Deemter
当流速较小时，H≈B/u,分子扩散项(B项) 就成为色谱峰扩张的主要因素，此时应采用分子量较大的载气 (N2、Ar)，使组分在载气中有较小的扩散系数。而当流速较大队 H≈C u,传质项(C项)为控制因素，宜采用低分子量的载气(H2、He)，此 时组分在载气中有较大的扩散系数，可减小气相传质阻力，提高柱 效。选择载气时还应考虑对不同检测器的适应性。 对于填充柱，N2的最佳实用线速为10~12cm／s, H2为15~ 20cm／s, 通常载气的流速习惯上用柱前的体积流速(mL／min) 来表示，也可通过皂膜流量计在柱后进行测定。若色谱柱内径 为3mm，N2的流通一般为40~60mL／min，H2的流速为60~90 mL／min。

67 ▲Selection of column temperature(自学）
Understand how to select column temperature ▲Properties and amount of stationary liquid（自学） What influence does stationary liquid have, How to select? Requirement for mixed liquids, separation characterization ▲Properties and size of supports（自学） Definition of support, requirement for support, how to select it? ▲Injection time and injection amount（自学） How do they affect peak shape? How to select them?

68 §2-5 Detectors of GC (Concentration sensitive detector & mass flow rate sensitive detector)

69 ▲Thermal conductivity detector(热导池检测器，TCD)
Self-study & Exam: 热导池的构造，工作原理及影响检测灵敏度的因素。

70 结构简单，灵敏度高，响应快， 稳定性好，线形范围宽（10-6）.
▲Hydrogen flame ionization detector(氢火焰离子化检测器,FID) 氢火焰电离化检测器，简称氢焰检测器。 对大多数有机化合物有很高的灵敏度，一般比热导池检测器的灵敏度高几个数量 级，能检测至ppb级(10-12g.s-1)的痕量物质，故适宜于痕量有机物的分析。 结构简单，灵敏度高，响应快， 稳定性好，线形范围宽（10-6）. Self-study & Exam: 结构、作用原理、操作条件

71 ▲Electron capture detector(电子俘获检测器，ECD)
▲Flame photometric detector(火焰光度检测器，FPD) FPD is highly sensitive and highly selective to the compounds containing sulphur, phosphor, etc. 检测器

72 ●检测器的性能指标 Self-study & Exam 检测器的灵敏度、检出限，最小检出量、响应时间、线形范围等的概念，物理意义，计算公式等。

73 §2-6 Qualitative analytical methods for GC
●Qualitative analysis based on chromatographic rotention value ▲直接根据色谱保留值进行定性 各种物质在一定的色谱条件下（固定相、操作条件）均有确定的保留值，可以作为定性指标。 适合于已知混合物及已确定存在范围或类型的化合物的鉴定 对于完全未知的化合物鉴定，可靠性较差。 方法的可靠性与色谱柱的分离效率（柱效）有密切关系 常采用仅与柱温有关，而与操作条件（柱长、固定液含量、载气流速等）无关，重现性较好的相对保留值r21作为定性指标。

74 保留指数法（rotention index, Kovats index)
与文献值比较 与标准样对照 混合进样: 将标准样与未知物混合进样，通过观察是否有新峰出现，或未知峰上是否出现分叉等现象，判断未知物与标准样是否属同一物质。 多柱法： 通过多根不同性质的色谱柱分离实验，确定标准样与未知样是否属同一物质。不同物质在同一根色谱柱上可能具有相同的保留值。 保留指数法（rotention index, Kovats index) Seen in next page

75 保留指数I： I = 100 lgXi – lgXZ lgXZ+1 – lg XZ + Z
用两个紧靠近待测物质的标准物（一般选用两个相邻的正构烷烃）标定被测物质，并使用均一标度（即不用对数），用下式定义： I = 100 lgXi – lgXZ lgXZ+1 – lg XZ + Z X为保留值（tR’, VR’,或相应的记录纸距离），下脚标i为被测物质，Z, Z+1为正构烷烃的碳原子数，XZ < Xi < XZ+1，IZ = Z × 100

76 EXAMPLE n-heptane: n-octane: Z = 7 Figure Sketch map for determination
of rotention index EXAMPLE From the right figure, following data can be gotten n-heptane: Butyl ester acetate: n-octane: Z = 7

77 I TC A B X1 • X2 GC-MS, GC-IR, GC-chemical analysis •

78 §2-7 Quantitative analysis of GC
Under given chromatographic conditions, mass( or concentration in carrier gas) of analyte is directly proportional to response signal of the detector (chromatographic peak area or height): mi = fi′• Ai fi′refers to quantitative calibration factor

79 ●Peak area measurements
1. Peak area equals to product of peak height and peak width at half height A = h • Y1/2 上式计算得到的峰面积仅为实际面积的0.94倍，实际峰面积应为： A = 1.065h •Y1/2 不过，在相对计算时，1.065常可以忽略 特点： 快速、简便，但不适合于不对称峰、窄峰、极弱峰。

80 2. Product of peak height and peak width at peak base
A ≈ h × Y 用本方法测得的峰面积约为真实面积的0.98倍。 本方法适用于矮宽峰。 3.Average peak width method(平均峰宽法) A = h × Y Y = (Y Y0.85) /2 本方法适用于不对称峰（asymmetrical)

81 Y1/2 ∝tR 4.Product of peak height and rotention time Y1/2 =btR
Under given operation conditions, peak width at half-height of 同系物 is proportional to rotention time: Y1/2 ∝tR Y1/2 =btR A = h•Y1/2 = bhtR 相对计算时，常数b可以省略。 特点：简便、快速，适用于狭窄峰，工厂控制分析。

82 ●Quantitative calibration factor
5.积分仪（integral meter) Simple、convenient、fast、exact（precision ranges 0.2%~ 2%)，and linear range wide ●Quantitative calibration factor 通常，同一检测器对不同物质的响应值不同，相同质量的不同物质往往具有不同的峰面积，因而不能直接用峰面积来计算被测物质含量。因此需要对仪器响应值进行校正。 mi = fi’ Ai fi’ = mi / Ai fi’ 为绝对质量校正因子，表征单位面积所代表的物质质量，由仪器的灵敏度决定，一般不易准确测定。实际工作中常用相对校正因子。

83 Relative calibration factor
Ratio of absolute calibration factors of the analyte and standard substance For TCD, benzene employed as standard For FID, n-heptane as standard Based on sought-out component’s units, following concepts are employed: Mass calibration factor Molar calibration factor Volume calibration factor

84 1.Mass calibration factor fm
f’i(m) f’s(m) Asmi Aims = Where I,s respectively refers to sought-out and standard substances 2.Molar calibration factor fM fM = f’i(M) f’s(M) AsmiMs AimSMi = = fm• MS Mi 各物质的量以摩尔数计，MS,Mi分别表示被测物与标准物质的相对分子质量（摩尔质量）

85

86 3.Volume calibration factor fV

87 4.Relative response value s’
Ratio of response values (sensitivity) of the substance i and standard sample s. When same unit is used, it is reciprocal of calibration factor. s’ = 1 / f’ s’, f’ only rely on properties of test sample, standard substance and type of detector, but not operation condition, cloumn temperature, flow rate of carrier gas, property of stationary liquid. Measurement of calibration factor Accurately weigh sought-out component and standard substance, after mixing, inject, analyze and determine corres-ponding peak area, and then calculate calibration factors using above equations.

88 ●Quantitative calculation methods in common use
（External standard method) （Internal standard method) （Normalization method) 外标法（定量进样-标准曲线法） （Internal standard curve method) 内标标准曲线法 内标法 归一化法 ●Quantitative calculation methods in common use

89 ●归一化法(Normalization method)
When all of the components can flow out the column and and show chromatographic peaks, the contents of all of the components could be determined by normalization method. If the sample consists of n components, and mass of each component is respectively m1,m2,…, mn, sum of all components m is 100%, then mass fraction wi of component i can be calculated by following expression: wi= mi m ×100% m1+m2+…+mn = Ai fi A1fi + A2f2 + … + Anfn ×100% mi mi i =

90 wi= mi m ×100% m1+m2+…+mn = Ai fi mi A1fi + A2f2 + … + Anfn mi ×100%
If fi is mass calibration factor, then wi stands for mass fraction, and if fi is molar calibration factor, then wi molar fraction or volume fraction (for gas sample).

91 Back

92 ●内标法（Internal standard method)

93 所以

94 特点： ▲适用于仅需测定部分组分或试样中其它组分不能全部出峰的情况 ▲可消除由于操作条件变化而引起的误差，准确度高 ▲每次分析均需准确测量，故不适合快速控制分析 内标物质的选择： ● ● ● ● Back

95 wi ∝ Ai/AS ●内标标准曲线法（Internal standard curve method)
如果经常需要测定同一物质，可固定试样的称取量，并加入恒定量的内标物，此时fimS/fsm为一常数 故： (or w) Figure Internal working graph wi ∝ Ai/AS 适合于液体试样的常规分析 Back

96 ●外标法（定量进样-标准曲线法，External standard method)
所谓外标法就是应用欲测组分的纯物质来制作标准曲线。此时用欲测组分的 纯物质加稀释剂(对液体样品用溶剂稀释、气体样品用载气或空气 稀释)配成不同含量(％)标准溶液，取固定量标准溶液进样分析，从所得色谱图上测出响应讯号(峰面积或峰高等)、然后绘制响应 汛号(纵坐标)对百分含量(横坐标）的标准曲线。分析试样时，取和制作标淮曲线时同样量的试样(固定量进样)，测得该试样的响应讯号，由标准曲线即可查出其百分含量。 Signal wi Ai

97 wi A ws As wi = ws Ai As wi = Ki × Ai
单点校正法（Single dot calibration method) 当被测试样中各组分浓度变化范围不大时，可不必绘制标准曲线，而用单点校正法。即配 制一个和被测组分含量十分接近的标准溶液，定量进样，由被测组 分和外标组分峰面积比或峰高比来求被测组分的含量： wi A ws As = wi = ws Ai As 由于S为标样，wS 和AS和均为已知 故，令Ki=wS /AS, 则： wi = Ki × Ai Ki为组分i的单位面积质量分数校正值。

98 §2-8 Capillary column gas chromatography
Self-study Problems: ■Differences between capillary column GC and packing column GC ■毛细管色谱柱分为哪几种类型？ ■毛细管柱有那些特点？

99 §2-9 characteristics and applications of GC
■High analytical efficiency ■High selectivity ■High sensitivity ■Simple operation ■Wide applications

100 High analytical efficiency & Selevtivity
Based on partition of the components on double phases time after time Packing column of 1~2m, n ≈ 103 Capillary column, n ≈ 106 For example, simultaneously separating and analyzing a mixture including more than 100 components at one time using a a hollow capillary column. 返回

101 High sensitivity For GC, mass sensitivity: ~ 10-13g 10-6 ~ 10-10(mass fraction) of impurities in ultra-pure gas, in monomer of polymer, and ultra-pure reagents can be detected. 10-6 ~ 10-9 (mass fraction) of pollutants in atmosphere can be directly detected. 10-6 ~ 10-9(mass fraction) of halide, sulfide, phosphide in foods, water sample and so on. Back

102 Simple and fast operation
Several minutes to tens of minutes each test Easy to automation back

103 Wide applications Practicable for analyzing all kinds of gas samples, volatile ( or able to be transformed into volatile compound) liquid or solid samples Including: Organic, inorganic compounds with a boiling point lower than 500℃ and a molecular weight less than 400, and a good thermal stability. Splitting gas chromatography and reaction gas chromatography extend the application fields of GC

104 Exercises

105 Back