Optimization & Monitoring.

Optimization & Monitoring

How to achieve optimal conditions?
1) Use knowledge about chromatography to select conditions 2) Optimize your system by doing experiments 3) After optimization, monitor the system so you are sure the conditions stay optimal

How to avoid chromatographic overlaps
Detector signal 1 2 3 4 5 6 7 8 9 10 min

How to avoid chromatographic overlaps Rules of thumb (general):
If the compounds differ in type or number of functional groups: try to change selectivity If the compounds are isomers: increase the efficiency In complex chromatograms: increase the efficiency

How to avoid chromatographic overlaps
B Peak resolution Rs = tR(B) – tR(A) (wb(A) + wb(B)) 1 2 A Peak overlap B B A A Increase efficiency (decrease peak width) Change selectivity (increased tR)

How to change selectivity in LC
Change solvent composition Change type of stationary phase B A Detector signal 1 2 3 4 5 6 7 8 9 10 min

How to change selectivity in LC
Change solvent composition Change type of stationary phase Selectivity issues depend on the applications. Understanding selectivity requires a good understanding of how the analytes interacts with both the stationary phase and the mobile phase  A good understanding of chemistry is required. B A Detector signal 1 2 3 4 5 6 7 8 9 10 min

How to achieve high column efficiency in LC
B A Detector signal 1 2 3 4 5 6 7 8 9 10 min

Solvent flow Increase column length Decrease particle diameter Uniform particles (Lower solvent strength) (Optimal mobile phase velocity)

Solvent flow Increase column length Decrease particle diameter Uniform particles (Lower solvent strength) (Optimal mobile phase velocity) Van Deemter equation Purnell equation Rs = N 4 α–1 α k(B) 1+k(B) H = A + B u + C∙u

Increase column length Decrease particle diameter Uniform particles (Lower solvent strength) (Optimal mobile phase velocity) Van Deemter equation Purnell equation Rs = N 4 α–1 α k(B) 1+k(B) H = A + B u + C∙u

Solvent flow Increase column length Decrease particle diameter Uniform particles (Lower solvent strength) (Optimal mobile phase velocity) Van Deemter equation Purnell equation Rs = N 4 α–1 α k(B) 1+k(B) H = A + B u + C∙u

Solvent flow Increased time Pressure limitations Increase column length Decrease particle diameter Uniform particles (Lower solvent strength) (Optimal mobile phase velocity) Pressure limitations Always good Increased time Van Deemter equation Purnell equation Rs = N 4 α–1 α k(B) 1+k(B) H = A + B u + C∙u

Solvent flow HPLC: Typical particle diameters of 2-5 m. Pressures up to 400 bar. UHPLC (Ultra high performance LC) Particle diameters < 2 m. Pressures above 400 bar. Monodisperse particles (all same size).

How to increase efficiency in gas chromatography
Increase column length Decrease column diameter Decrease film thickness (Lower temperature) (Optimal carrier gas velocity) Low efficiency per meter High efficiency per meter Golay equation Purnell equation Rs = N 4 α–1 α k(B) 1+k(B) B u H = + C∙u

High efficiency per meter Low efficiency Increase column length Decrease column diameter Decrease film thickness (Lower temperature) (Optimal carrier gas velocity) Golay equation Rs = N 4 α–1 α k(B) 1+k(B) Purnell equation B u H = + C∙u

High efficiency per meter Low efficiency Increased time Pressure limitations Increase column length Decrease column diameter Decrease film thickness (Lower temperature) (Optimal carrier gas velocity) Pressure limitations Decreased sample capacity Decreased sample capacity Increased time Golay equation Rs = N 4 α–1 α k(B) 1+k(B) Purnell equation B u H = + C∙u

Data for apolar column (kanalyte = 5) Internal Diameter (mm) Film Thickness (m) Plates per meter 0.10 11980 0.18 6660 0.25 4630 0.32 3760 0.45 2840 0.53 2060 Phase ratio, β = 1000 High efficiency per meter Low efficiency per meter

Data for apolar column (kanalyte = 5) Internal Diameter (mm) Film Thickness (m) Plates per meter 0.10 11980 0.18 6660 0.25 4630 0.32 3760 0.45 2840 0.53 2060 10 m column  plates 25 m column  plates Phase ratio, β = 1000 High efficiency per meter Low efficiency per meter

How to change selectivity in GC
Change type of stationary phase (the mobile phase has no selectivity) The mobile phase has no selectivity and there are a limited number of stationary phase types. Understanding and predicting selectivity in GC is therefore much simpler than in LC (Good chemists do LC, bad chemists do GC) B A Detector signal 1 2 3 4 5 6 7 8 9 10 min

Time/resolution tradeoff
In chromatography there is usually a tradeoff between time and resolution (or efficiency) We want as short runs as possible (time=money) but with sufficient resolution Acceptable resolution Acceptable resolution And half the time

In chromatography there is usually a tradeoff between time and resolution (or efficiency) We want as short runs as possible (time=money) but with sufficient resolution If we want to sacrifice chromatographic efficiency to save time there are several options: Reduce the column length Use higher than optimal mobile phase velocity Increase mobile phase strength (LC) or temperture (GC) Use steeper gradients of solvent strength or temperature

Which of the two options that is the best choice will depend on the conditions used and the importance of the C term relative to the A and B terms. The penalty for using higher than optimal velocity depends on the steepness of the curve (C-term)

Which of the two options that is the best choice will depend on the conditions used and the importance of the C term relative to the A and B terms. The penalty for using higher than optimal velocity depends on the steepness of the curve (C-term) The general advice for GC is to always use optimal velocity and reduce the column length. That is also cheaper since there will be less carrier gas consumption and since shorter columns are cheaper than long columns.

Which of the two options that is the best choice will depend on the conditions used and the importance of the C term relative to the A and B terms. The penalty for using higher than optimal velocity depends on the steepness of the curve (C-term) The general advice for GC is to always use optimal velocity and reduce the column length. That is also cheaper since there will be less carrier gas consumption and since shorter columns are cheaper than long columns. However, if the column is used for several methods with different requirements for efficiency, it is usually more convenient to use higher than optimum flow.

Which of the two options that is the best choice will depend on the conditions used and the importance of the C term relative to the A and B terms. The penalty for using higher than optimal velocity depends on the steepness of the curve (C-term) In LC the C term is low with small particles <5 μm and the mobile phase flow will usually be higher than optimum. In LC, pressure limitations of the pump may be more important for the conditions chosen than the C term in the van Deemter equation.

1) Use knowledge about chromatography to select conditions 2) Optimize your system by doing experiments 3) After optimization, monitor the system so you are sure the conditions stay optimal

Why do we have to do experiments when we have so much theory and so many nice equations to tell us which conditions that are optimal?

Why do we have to do experiments when we have so much theory and so many nice equations to tell us which conditions that are optimal? 1) Because theory will not always fit reality 2) Because we will not have good enough knowledge about the system we are working with

Why do we have to do experiments when we have so much theory and so many nice equations to tell us which conditions that are optimal? 1) Because theory will not always fit reality 2) Because we will not have good enough knowledge about the system we are working with We will not know exact column dimensions, exact particle diameters, exact diffusion coefficients, exact flow rates and contribution to extra-column effects from the chromatographic system.

Linear flow rates, pressures and volumes In GC, flow rate is adjusted from the head pressure, column dimensions are critical In LC a constant volume is delivered, but the volume of the column that is occupied by the stationary phase is often difficult to estimate.

Optimization Best performance Low performance

Optimization Using chromatographic knowledge and making clever choices
Best performance Using chromatographic knowledge and making clever choices (and having enough money to buy the right equipent) Low performance

Optimization Experimenting and modelling
Best performance Low performance Experimenting and modelling Using chromatographic knowledge and making clever choices (and having enough money to buy the right equipent)

 You have to do experiments
Optimization  You have to do experiments But how?

 You have to do experiments
Optimization  You have to do experiments But how? There are many ways to optimize chromatographic separations. But the general methodology is to do experimental design and calculate response surfaces

Optimization  You have to do experiments But how?
Experimental design is a systematic way of setting up your experiments

Optimization Response surfaces
A response surface tells you how the response (that you want to optimize) varies with different parameters

Optimization Response surfaces response variable Measured
Varied parameter 1 Varied parameter 2

Optimization Response surfaces Surface plot Contour plot
response variable Measured Contour plot Varied parameter 1 Varied parameter 2

Optimization Response surfaces Maximum response variable Measured
Varied parameter 1 Varied parameter 2

Finding the response surface
Optimization Finding the response surface response variable Measured Varied parameter 1 Varied parameter 2 x1 x2 y

Optimization y = b0 + b1x1 + b2x2 + b12x1x2 + b11x12 + b22x22
Finding the response surface means that you have to solve an eqation explaining how the response, y, varies as function of the x-variables, the interactions between the variables and usually also higher order (squared) terms of the main variables The regression coefficients, b, are found for instance by multivariate regression y = b0 + b1x1 + b2x2 + b12x1x2 + b11x12 + b22x22

Optimization y = b0 + b1x1 + b2x2 + b12x1x2 + b11x12 + b22x22
The number of experiments must be equal or higher than the number of regression coefficients  the number of experiments increase with the number of variables and the complexity of the surface y = b0 + b1x1 + b2x2 + b12x1x2 + b11x12 + b22x22

For three independent variables:
Optimization The number of experiments must be equal or higher than the number of regression coefficients  the number of experiments increase with the number of variables and the complexity of the surface y = b0 + b1x1 + b2x2 + b12x1x2 + b11x12 + b22x22 For three independent variables: y = b0 + b1x1 + b2x2 + b3x3 + b12x1x2 + b23x2x3 + b13x1x3 + b11x12 + b22x22 + b33x32

Setting up an experimental design for optimization
Start by defining a point where you believe that the optimal conditions are most likely to be This is your centre pont Variable 2 Variable 1

Start by defining a point where you believe that the optimal conditions are most likely to be This is your centre pont You thereafter define a region where you expect that it is probable that the optimum can be found This is your experimental domain Variable 2 Variable 1

You thereafter set up an experimental design that will cover the experimental domain in a best possible way Variable 2 Variable 1

You thereafter set up an experimental design that will cover the experimental domain in a best possible way There are three designs that are common in chromatographic optimization: Variable 2 Variable 1

You thereafter set up an experimental design that will cover the experimental domain in a best possible way There are three designs that are common in chromatographic optimization: Factorial design Variable 2 Variable 1

You thereafter set up an experimental design that will cover the experimental domain in a best possible way There are three designs that are common in chromatographic optimization: Factorial design Central composite design Variable 2 Variable 1

You thereafter set up an experimental design that will cover the experimental domain in a best possible way There are three designs that are common in chromatographic optimization: Factorial design Central composite design Doehlert design Variable 2 Variable 1

Variable 2 Note that the factorial design has too few experimental points to solve response surfaces with both squared terms and interactions  It can only be applied on less complex surfaces Variable 1

Optimization Factorial design Central composite design Doehlert design
With three variables the corresponding designs look like this

Mixture designs

Mixture designs When optimizing mobile phase composition in LC it is necessary to apply mixture designs, where the variables are not independent (because the sum is always 100%)

Mixture designs When optimizing mobile phase composition in LC it is necessary to apply mixture designs, where the variables are not independent (because the sum is always 100%) 100 % solvent A 50/50/0 50/0/50 33/33/33 100 % solvent B 0/50/50 100 % solvent C

Mixture designs Acetonitrile
Example of optimization of mobile phase selectivity using a mixture design with three solvents From D.C. Harris, Quantitative Chemical Analysis, 8th ed., Freeman) Methanol Tetrahydrofuran

Stepwise optimization Stepwise search for maximum
The simplex method

The simplex method Start by defining three experiments

Stepwise optimization
Stepwise search for maximum The simplex method Reflect the worst point around the line between the two best points

The simplex method Repeat the process

Stepwise search for maximum The simplex method The simplex will gradially ”climb” towards maximum

The simplex method This is the simplest form of simplex optimization. More advanced algorithms have rules for expanding and contractiong the designs so that it moves more rapidly and converges around the maximum Because you have to do new calculations after each experiment it is usually not an efficient method in chromatography (since autosamplers allow us to do many experiments in one sequence)

The simplex method Simplex tutorial:

You can also do stepwise optimization using the Doehlert design

You can also do stepwise optimization using the Doehlert design If the model indicates that the maximum is outside the investigated domain you can move the design in that direction, but reuse some of the experiments

In mixture designs you can constrain the experimental domain to the triangle where the optimum was found optimum

In mixture designs you can constrain the experimental domain to the triangle where the optimum was found

Which parameters should we optimize for?
Optimization Which parameters should we optimize for?

Optimization Which parameters should we optimize for? Optimal conditions in chromatography is usually a tradeoff between efficiency and time

Optimization Which parameters should we optimize for? Optimal conditions in chromatography is usually a tradeoff between efficiency and time Optimizing for resolution alone may give you unecessary long (time consuming) chromatographic runs

Optimization Which parameters should we optimize for? Optimal conditions in chromatography is usually a tradeoff between efficiency and time Optimizing for resolution alone may give you unecessary long (time consuming) chromatographic runs The Purnell equation: Increasing k will increase resolution

Optimization Which parameters should we optimize for? Optimal conditions in chromatography is usually a tradeoff between efficiency and time Optimizing for resolution alone may give you unecessary long (time consuming) chromatographic runs The Purnell equation: Optimal N may require impractically low flow rates (in LC)

Optimization Which parameters should we optimize for? Optimal conditions in chromatography is usually a tradeoff between efficiency and time Optimizing for resolution alone may give you unecessary long (time consuming) chromatographic runs The Purnell equation: It is therefore a often a good idea to optimize for selectivity and to make separate models that can tell you if efficiency is good enough

Optimization Which parameters should we optimize for? Optimal conditions in chromatography is usually a tradeoff between efficiency and time Optimizing for resolution alone may give you unecessary long (time consuming) chromatographic runs If you have many peaks it is not easy to optimize for selectivity. Solving one problem may create new ones.  Optimize for efficiency

Example of responsesurface design in GC
… from an EMQAL master project [Chhaganlal, Skartland & Mjøs, J. Chromatogr. A 1332 (2014) 64–72.]

Example of responsesurface design in GC
… from an EMQAL master project [Chhaganlal, Skartland & Mjøs, J. Chromatogr. A 1332 (2014) 64–72.] Transfer of retention pattern of Fatty acid methyl esters from GC-MS to GC FID We identify the compounds by GC-MS and calculate retention indices When we later analyse the samples by GC-FID we would like to have the same retention indices so that we are confident about the identities.

Target pattern from GC-MS
Stating the problem Direct transfer of conditions from GC-MS to GC-FID Same column type and dimensions Same temperature program Same carrier gas velocity Outlet pressure compensation (GC-MS: 0 Atm, GC-FID: 1 Atm.) Pattern from GC-FID Target pattern from GC-MS

Stating the problem

Stating the problem More that two peak widths (4σ) from the targets

Stating the problem We would like to be able to replace columns, change column dimensions, change outlet pressure (MS or FID), and change carrier gas (He, H2) and keep exactly the same retention patterns (i.e. same retention indices) Different compounds require different shifts  cannot be solved with e.g. retention time locking (flow compensation)

Stating the problem Some stationary phases change their properties with temperature (Apparent) polarity of GC columns as a function of temperature. Castello, Vezzani, D’Amato (1997) J. Chromatogr. A 779, p The properties of the columns will also change with time

Stating the problem BPX-70 Fatty acid methyl esters (FAME) are usually analyzed on cyanopropyl columns, such as BPX-70, or on polyethylene glycol columns (PEG). Using columns that changes selectivity with temperature gives some advantages, because small changes in the temperature or flow conditions can resolve overlaps. But the reproducibility of retention patterns is a challenge. PEG

Methodology We use simple temperature programs where the start temperature of the temperature rate, steepness of the temperature rate and the carrier gas velocity can be varied. 40 60 80 100 120 140 160 180 200 220 240 260 10 20 30 50 60 min Start temp, x1 Rate, x2 °C Temperature program BPX-70 (usually 60 m, 0.25 mm, 0.25 μm) Increased start temperature (x1) increases polarity of the column with higher effect on early eluting compounds. Increasing temp. rate (x2) increases polarity with approximately equal effect on all compounds

Methodology 40 60 80 100 120 140 160 180 200 220 240 260 10 20 30 50 60 min Start temp, x1 Rate, x2 °C Rate Start temperature The start temperature and the rate is varied around conditions that we believe would give an accurate reproduction of the retention pattern.

Methodology y = b0 + b1x1 + b2x2 + b12x1x2 + b11x12 + b22x22
40 60 80 100 120 140 160 180 200 220 240 260 10 20 30 50 60 min Start temp, x1 °C Rate, x2 Rate Start temperature y = b0 + b1x1 + b2x2 + b12x1x2 + b11x12 + b22x22 A Doehlert design with two variables requires seven experiments

Typical experimental values
GC conditions Typical experimental values (60 m BPX-70 column)

Calculations Retention times of the fatty acids in the calibration mixture for the seven experiments  converted to retention indices (Equivalent chain lengths, ECL) Retention time Equivalent chain lengths (ECL)

Calculations For each compound, establish the relationship between chromatographic parameters and retention (ECL)

Models of ECL, individual
The model for ECL for the fatty acid 18:3 n-3 Rate Start temp

The model for ECL for the fatty acid 18:3 n-3 The ECL value of 18:3 n-3 in the pattern we would like to reproduce (the target pattern) is 19.83 Rate Start temp

The model for ECL for the fatty acid 18:3 n-3 The ECL value of 18:3 n-3 in the pattern we would like to reproduce (the target pattern) is 19.83 Subtracting this value gives us the target surface Rate Start temp The target surface shows the difference between what we can expect at different conditions (start temperature and gradient) and what we want (our target)

The model for ECL for the fatty acid 18:3 n-3 The ECL value of 18:3 n-3 in the pattern we would like to reproduce (the target pattern) is 19.83 Subtracting this value gives us the target surface Rate Start temp Trace of acceptable conditions ΔECL<0.002 ECL units

Different target surfaces

Different target surfaces
If we look at the traces for the optimal conditions for several fatty acids we see that there is a region where they meet Traces for individual FAMEs (<0.04 ECL units from target)

Start of temperature gradient
Common target surface 120 140 160 180 200 1 2 3 16:1 n–7 18:3 n–3 20:5 n–3 22:6 n–3 Start of temperature gradient (C) Temperature gradient (C/min) Individual target surfaces are summarized into a common target surface

Temperature rate 1.08 °C/min
Common target surface Rate Start temp Optimal conditions Start temperature °C Temperature rate 1.08 °C/min

Validation of pred. optimum The predicted conditions tested

Validation of pred. optimum

Validation results Direct transfer of conditions compared with validated results after calibration. Repeatability is the difference in ECL by repeating the center point in the design when predicted conditions were validated. 0.07 0.18 Mean error Max error 0.16 0.06 0.14 0.05 0.12 0.04 0.10 Error without proper optimization ∆ ECL Error without proper optimization ∆ ECL Error with proper optimization Error with proper optimization 0.03 0.08 0.06 0.02 0.04 0.01 0.02 0.00 0.00 Repeatability All Smpl Direct Repeatability All Smpl Direct

Model of separation efficiency
(separation number)

Monitoring & Control charts
Keep in mind that when you have found your optimal conditions it it necessary to make sure that the system stays there

Analyse control sample(s) at regular intervals The results should be randomly distributed around the mean (usually with a normal distribution curve) 10.0 9.5 9.0 8.5 8.0  7.5 7.0 6.5 6.0 5.5 5.0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 observations

Analyse control sample(s) at regular intervals The results should be randomly distributed around the mean (usually with a normal distribution curve) If rare observations: Check 10.0 9.5 9.0 8.5 8.0  7.5 7.0 6.5 6.0 5.5 5.0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 observations

Analyse control sample(s) at regular intervals The results should be randomly distributed around the mean (usually with a normal distribution curve) If rare observations: Check If very rare observations: Stop (or discard results) 10.0 9.5 9.0 8.5 8.0  7.5 7.0 6.5 6.0 5.5 5.0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 observations

What is a rare observation? If rare observations: Check If very rare observations: Stop (or discard results) 10.0 9.5 9.0 8.5 8.0  7.5 7.0 6.5 6.0 5.5 5.0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 observations

What is a rare observation? μ-3σ μ-2σ μ-σ μ μ+σ μ+2σ μ+3σ 99.7% 95.4% 68.3% If rare observations: Check If very rare observations: Stop (or discard results) 10.0 9.5 9.0 8.5 8.0  7.5 7.0 6.5 6.0 5.5 5.0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 observations

What is a rare observation? Observations outside 3s has a probability of 0.3% 10.0 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 +3s +2s +s  –s –2s –3s observations 9.5 9.0 8.5 8.0 7.5 7.0 6.5 6.0 5.5 5.0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 observations

What is a rare observation? Observations outside 3s has a probability of 0.3% Observations outside 2s has a probability of 4.6% 10.0 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 +3s +2s +s  –s –2s –3s observations 9.5 9.0 8.5 8.0 7.5 7.0 6.5 6.0 5.5 5.0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 observations

What is a rare observation? Observations outside 3s has a probability of 0.3% Observations outside 2s has a probability of 4.6% 10.0 Action line Warning line 9.5 9.0 8.5 8.0 7.5 7.0 6.5 6.0 5.5 5.0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 observations

What is a rare observation? Observations outside 3s has a probability of 0.3% Two consecutive on the same side outside warning: 0.05% 10.0 Action line Warning line 9.5 9.0 8.5 8.0 7.5 7.0 6.5 6.0 5.5 5.0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 observations

What is a rare observation? Observations outside 3s has a probability of 0.3% Two consecutive on the same side outside warning: 0.05% 2 of 3 outside warning 7 consecutive on the same side of the center line 6 consecutive in increasing or decreasing order 10.0 10.0 Action line Warning line 9.5 9.5 +3s +2s +s  –s –2s –3s 9.0 9.0 8.5 8.5 8.0 8.0 7.5 7.5 7.0 7.0 6.5 6.5 6.0 6.0 5.5 5.5 5.0 5.0 1 1 6 6 11 11 16 16 21 21 26 26 31 31 36 36 41 41 46 46 51 51 56 56 61 61 66 66 71 71 76 76 81 81 86 86 91 91 96 96 observations observations

Monitoring & Control charts Which parameters should be monitored?

Monitoring & Control charts Which parameters should be monitored?
Dependent on the application. Usually resolution between critical peaks, efficiency and peak asymmetry are useful indicators The first indication that a good column is becoming bad is usually peak tailing, so Af or Tf is an obvious choice in most cases

Summary

Summary Chromatographic systems are not magic boxes with impredictable behaviour

Summary Chromatographic systems are not magic boxes with impredictable behaviour The quality of separations can be measured and optimized (and understood)

Summary Best performance Chromatographic systems are not magic boxes with impredictable behaviour The quality of separations can be measured and optimized (and understood) There are tools you can use to get from low performance to high performance Low performance

Summary Best performance Purnell equation Van Deemter equation
Low performance

Summary Best performance And when you have found the best conditions, make sure that you stay there Low performance

Summary There are two important models that is (quite) general in chromatography and critical for the performance Purnell equation Van Deemter equation Rs = 2 (tR(B) – tR(A)) wb(A) + wb(B) t wb N = 16 tR wb 2 tR(B) tR(A) ′ α = = k(B) k(A) k = = ns nm tR tM ′

Summary And there are some additional equations that can be used to monitor the system Separation number Peak capacity Isothermal retention index Temperature programmed retention index Asymmetry factor Tailing factor

Optimization & Monitoring.

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