# Separation of Molar Weight-Distributed Polyethylene Glycols by Reversed-Phase Chromatography—II. Preparative Isolation of Pure Single Homologs

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Thermodynamic Retention Model

#### 2.2. Column Model Based on Discrete Convolution

#### 2.3. Linear Solvent Strength Theory

## 3. Experimental

#### 3.1. Materials

#### 3.2. Preparative Chromatography

#### 3.3. Analytical Chromatography

## 4. Results and Discussion

#### 4.1. Separation Problem and Role of Operating Conditions

#### 4.2. Thermodynamic Analysis

#### 4.3. Separation under Linear Conditions

#### 4.4. Separation under Nonlinear Conditions

#### 4.4.1. Isocratic Operation

#### 4.4.2. Gradient-Based Operation

## 5. Summary and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**MWD of PEG 1000 determined by LC/MS (symbols) and interpolation by a normal distribution (line; mean value 22.285, standard deviation 3.81). Measured using the analytical column (eluent 20 vol% ACN, 1 mL/min; 25 ${}^{\circ}$C; injection 10 $\mathsf{\mu}$L of 1 g/L PEG 1000 in water).

**Figure 2.**Example chromatograms demonstrating the roles of temperature and mobile phase composition for the separation of PEG 1000 on the preparative column. For better orientation, peaks are marked for the homologs with n = 15, 20, and 25. (

**Left**) three different temperatures (15, 30, 50 ${}^{\circ}$C) at 19 vol% ACN in water as eluent. (

**Right**) three different eluent compositions (15, 17, and 19 vol% ACN in water) at 30 ${}^{\circ}$C. Remark: The chromatogram in the left (middle) is the same as the one in the right (bottom). Samples: 50 $\mathsf{\mu}$L of 5 g/L PEG 1000 in water.

**Figure 3.**Determination of thermodynamic parameters for the separation of PEG 1000 on the preparative column for the example of an eluent with 17 vol% ACN. (

**Left**) van’t Hoff plot of data and linear regression against Equation (1) (lines) for the different homologs. (

**Right**) enthalpic and entropic contributions as a function of n corresponding to the slopes ($\Delta {H}_{n}^{\circ}$) and intercepts ($\Delta {S}_{n}^{*}$) of the lines in the left (symbols). Linear regression against Equation (2) (lines) delivers $\Delta {H}_{r}^{\circ}$, $\Delta {H}_{e}^{\circ}$, and $\Delta {S}_{r}^{*}$, $\Delta {S}_{e}^{*}$ as slopes and intercepts, respectively.

**Figure 4.**Comparison of thermodynamic parameters for the preparative and the analytical column as function of the mobile phase composition. Filled symbols—preparative column (for values see Table 2), open symbols—analytical column (data from [15]). Lines—interpolation by third-order polynomials. The coefficients are tabulated in the Supplementary Information.

**Figure 5.**Evaluation of the thermodynamic retention model for the preparative column at different conditions. Comparison of retention times for the chromatograms shown in Figure 2 (symbols) to the predictions by the thermodynamic retention model (lines).

**Figure 6.**Validation of the process model for the preparative column at two different conditions. Symbols—experimental data, lines—simulated total outlet concentration, ${\Sigma}_{i}\phantom{\rule{0.166667em}{0ex}}{c}_{out,i}\left(t\right)$, acc. to Equation (3). (

**Left**) experiment at 20 ${}^{\circ}$C. (

**Right**) experiment at 35 ${}^{\circ}$C. Other conditions: eluent 20 vol% ACN, sample 50 $\mathsf{\mu}$L of 5 g/L PEG 1000 in water. Simulation with averaged values for $NTP$ of 3330 (20 ${}^{\circ}$C) and 4670 (35 ${}^{\circ}$C).

**Figure 7.**Large-volume injections on the preparative column under strongly diluted conditions. Black—sample dissolved in the eluent. Orange—sample dissolved in pure water. For comparison, elution windows predicted by the thermodynamic model are marked for selected homologs. Conditions: 18 vol% ACN, 50 ${}^{\circ}$C, injection of 150 mL PEG 1000 with 0.05 g/L.

**Figure 8.**Overloading series under isocratic conditions for the preparative column. Overlay of five chromatograms with increasing injection concentrations ranging from 5 to 100 g/L (see legend) at an injection volume of 500 $\mathsf{\mu}$L, corresponding to injected amounts between 2.5 mg and 50 mg. For better orientation, the elution profiles for homolog n = 22 are marked. For comparison, the blue dashed lines mark the limiting retention times of the selected homologs for small injections calculated from the thermodynamic model. Measured at 18 vol% ACN and 30 ${}^{\circ}$C, the injection solvent is water.

**Figure 9.**Linear gradient experiment under diluted conditions (black) and comparison of retention times to the prediction by LLS theory (dashed blue lines). For better orientation, homolog n = 20 is marked. The orange line marks the solvent gradient (right axis). The dwell volume required to apply Equation (5) was measured as 11.4 mL. Conditions: Linear gradient from 15 vol% to 18 vol% ACN in 70 min, followed by a forced elution step at 70 min; 55 ${}^{\circ}$C; sample 50 $\mathsf{\mu}$L of 0.05 g/L PEG 1000 in water.

**Figure 10.**Experiment with four consecutively applied larger injections performed under linear gradient conditions. Conditions as in Figure 9, but injected concentration increased to 250 g/L.

**Figure 11.**Overlay of four preparative production runs performed with automated fraction collection to obtain the homologs, with n = 14 through n = 21 as products. Gray areas—Collected product fractions, blues dashed lines—retention times calculated from the LSS model. Fraction collector parameters: minimum peak height 2 pA, minimum start time 15 min. For chromatographic conditions, see Figure 10.

**Figure 12.**Analysis of the fractions collected during the preparative runs as marked in Figure 11.

**Top row**—Feed mixture (1 g/L PEG 1000 in water).

**Further rows**—Individual fractions. Conditions: analytical column, 20 vol% ACN, 25 ${}^{\circ}$C, 1 mL/min, injection volume 10 $\mathsf{\mu}$L.

**Figure 13.**Example for the separation of PEG 4000 by gradient chromatography on the preparative column. Baseline resolution up to at least n = 70 is achieved. Conditions: Linear gradient from 28 to 30 vol% ACN in 90 min, followed by isocratic elution with 30 vol% ACN; 55 ${}^{\circ}$C; sample 50 $\mathsf{\mu}$L of 200 g/L pEG 4000 in water.

**Table 1.**Role of the injection solvent. Dependency of ${k}^{\prime}$, $NTP$, and peak asymmetry, ${A}_{P}$, on the amount of acetonitrile in the injection solvent, ACN${}_{\phantom{\rule{3.33333pt}{0ex}}\mathit{inj}}$, for the example of homolog n = 20. Deviations in % from the corresponding value for 100% water as injection solvent. Conditions: Analytical column, eluent 20 vol% ACN, 50 ${}^{\circ}$C, 0.7 mL/min, samples: 10 $\mathsf{\mu}$L of 0.2 g/L PEG 1000.

ACN${}_{\phantom{\rule{3.33333pt}{0ex}}\mathit{inj}}$ | ${\mathit{k}}^{\prime}$ | $\mathbf{\Delta}{\mathit{k}}^{\prime}$ | $\mathit{NTP}$ | $\mathbf{\Delta}\mathit{N}\mathit{T}\mathit{P}$ | ${\mathit{A}}_{\mathit{P}}$ | $\mathbf{\Delta}{\mathit{A}}_{\mathit{P}}$ |
---|---|---|---|---|---|---|

vol% | - | % | - | % | % | |

0 | 12.35 | 14,000 | 1.11 | |||

10 | 12.25 | −0.8 | 12,810 | −8.5 | 1.19 | 7.2 |

20 | 12.22 | −1.1 | 10,070 | −28.1 | 1.29 | 16.2 |

35 | 12.18 | −1.4 | 6170 | −55.9 | 1.36 | 22.5 |

50 | 12.20 | −1.2 | 6010 | −57.1 | 1.37 | 23.4 |

**Table 2.**Determined thermodynamic parameters as function of the acetonitrile content (ACN) of the mobile phase.

ACN | $\mathbf{\Delta}{\mathit{H}}_{\mathit{r}}^{\circ}$ | $\mathbf{\Delta}{\mathit{H}}_{\mathit{e}}^{\circ}$ | $\mathbf{\Delta}{\mathit{S}}_{\mathit{r}}^{*}$ | $\mathbf{\Delta}{\mathit{S}}_{\mathit{e}}^{*}$ |
---|---|---|---|---|

vol% | kJ/mol | kJ/mol | J/(mol K) | J/(mol K) |

15 | 1.185 | −4.423 | 6.401 | −29.390 |

17 | 1.365 | −4.773 | 6.533 | −30.131 |

19 | 1.485 | −5.153 | 6.551 | −30.999 |

21 | 1.566 | −5.488 | 6.487 | −31.548 |

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**MDPI and ACS Style**

Supper, M.; Jost, R.; Bornschein, B.; Kaspereit, M.
Separation of Molar Weight-Distributed Polyethylene Glycols by Reversed-Phase Chromatography—II. Preparative Isolation of Pure Single Homologs. *Processes* **2023**, *11*, 946.
https://doi.org/10.3390/pr11030946

**AMA Style**

Supper M, Jost R, Bornschein B, Kaspereit M.
Separation of Molar Weight-Distributed Polyethylene Glycols by Reversed-Phase Chromatography—II. Preparative Isolation of Pure Single Homologs. *Processes*. 2023; 11(3):946.
https://doi.org/10.3390/pr11030946

**Chicago/Turabian Style**

Supper, Malvina, Rosanna Jost, Benedikt Bornschein, and Malte Kaspereit.
2023. "Separation of Molar Weight-Distributed Polyethylene Glycols by Reversed-Phase Chromatography—II. Preparative Isolation of Pure Single Homologs" *Processes* 11, no. 3: 946.
https://doi.org/10.3390/pr11030946