# Determination of Solubility Parameters of Ibuprofen and Ibuprofen Lysinate

^{1}

^{2}

^{*}

## Abstract

**:**

^{0.5}and with IGC it was δ

_{t}= 35.17 MPa

^{0.5}. However, the values of partial solubility parameters, i.e., δ

_{d}, δ

_{p}and δ

_{h}, did differ from each other, what might be due to the complex behaviour of a salt in the presence of various solvents.

## 1. Introduction

_{t}, as square root of the cohesive energy density (CED) of a substance. CED is an energy required to separate the atoms or molecules from each other and it’s a direct criterion of attractiveness [3]:

_{v}is the heat of vaporization, R is the gas constant, T is the temperature and V

_{m}is the molar volume.

_{coh}, on components arising from dispersion forces, E

_{d}, permanent dipole-dipole interactions, E

_{p}, and hydrogen bonds, E

_{h}[8]:

_{m}, and squared, it gives us a new three dimensional approach in which Hildebrand’s total solubility parameter squared is equal to the sum of the squares of Hansen’s components [8]:

_{d}, δ

_{p}and δ

_{h}are Hansen’s solubility parameters which represent the three main types of interactions in organic matter.

_{d}and δ

_{p}, and introduced new, combined solubility parameter, δ

_{v}:

_{v}as a function of δ

_{h}is called Bagley’s plot. The distance, R

_{a(v)}, in the Bagley’s plot, can be expressed by the following equation:

_{a(v)}should be in the range of R

_{a(v)}≤ 5.6 MPa

^{0.5}.

_{t}:

_{t}< 7 MPa

^{0.5}. They were also able to estimate the difference of total solubility parameters at which the mixing is not likely to occur, Δδ

_{t}> 10 MPa

^{0.5}[14]. Numerous studies have confirmed the validity of Greenhalgh’s approach [11,13,15,16,17], however, on the other hand some studies [18,19] have pointed out the deficiency of comparisons between total solubility parameters.

_{t}, for solvents, polymers and active substances, can be determined by many different ways, using different methods, all being applied in the existing literature. In order to obtain greater insight on interactions between substances, it is crucial to divide the total solubility parameter into the individual contributions (δ

_{d}, δ

_{p}and δ

_{h}), but there are only few methods for determination of all three partial solubility parameters. These correlations are still under research. In particular, the biggest limitation is the determination of partial solubility parameters of a drug, since most methods, used in the case of solvents and polymers, cannot be applied to drug molecules [20]. In this work we focused on determination of solubility parameters, using two different approaches: solely by calculation and an experimental approach.

#### 1.1. Calculation Methods

#### 1.2. Experimental Approach

#### 1.2.1. Extended Hansen’s Approach (EHA)

_{χ2}, with the solubility parameters of a drug:

_{0–6}are the coefficients of the regression analysis and ln

_{χ2}is a mole fraction solubility of a drug in a given solvent. Partial solubility parameters are then calculated using the constants of the regression analysis, C

_{0–6}:

#### 1.2.2. Inverse Gas Chromatography (IGC)

_{g}. Once the value of V

_{g}is obtained, chromatographic data can be converted into thermodynamic parameters using Equation (12) [26]:

_{r,1}, ${\mathrm{p}}_{1}^{0}$, B

_{11}, V

_{g}, V

_{1}, V

_{2}, ρ

_{1}, ρ

_{2}, represent the molecular mass, saturated vapor pressure, second virial coefficient, specific retention volume, molar volume and density of the solvent and solute, respectively.

_{1i}:

_{2}. Based on the given equation, δ

_{2}can also be calculated from the intersection with the abscissa $\left(\frac{{\mathsf{\delta}}_{2}^{2}}{RT}+\frac{{\mathsf{\chi}}_{s}^{\infty}}{{V}_{1}}\right)$.

_{n-alkanes}represents the value of the slope for the group of n-alkanes, m

_{1}represents the value of the slope for the group of polar solvents (aromatic hydrocarbons, ketones, 1-nitropropane, acetonitrile, 1,2-dichloroethane) and m

_{2}represents the value of the slope for the group of solvents with the ability to form hydrogen bonds (alcohols, pyridine, 1,2-dioxane).

## 2. Results

#### 2.1. Calculation Methods

#### 2.1.1. Ibuprofen

**Table 1.**Values of solubility parameters for ibuprofen by using six different group contribution methods.

Method | ||||||
---|---|---|---|---|---|---|

Hansen and Beerbower | Fedors | Hoftyzer and Van Krevelen | Hoy | Stefanis and Panayiotou | Just and Breitkreutz | Median δ_{t} (MPa^{0.5}) |

δ_{t} = 19.89 | δ_{t} = 20.91 | δ_{t} = 19.36 | δ_{t} = 19.71 | δ_{t} = 19.7 | δ_{t} = 19.20 | δ_{t} = 19.71 |

δ_{d} = 17.85 | δ_{d} = 17.56 | δ_{d} = 16.59 | ||||

δ_{p} = 2.22 | δ_{p} = 3.22 | δ_{p} = 4.27 | ||||

δ_{h} = 7.15 | δ_{h} = 8.31 | δ_{h} = 8.67 |

_{t}= 19.20 MPa

^{0.5}, was obtained by using the group contribution method of Just and Breitkreutz. The highest value, δ

_{t}= 20.91 MPa

^{0.5}, was obtained when using group contribution method of Fedors. The partial solubility parameters values also did not differ much between methods. The largest value in the case of the dispersion solubility parameter was obtained by using the group contribution method of Hoftyzer and Van Krevelen and the smallest value using the method of Just and Breitkreutz, where the values were δ

_{d}= 17.85 MPa

^{0.5}and δ

_{d}= 16.59 MPa

^{0.5}, respectively. The opposite trend had been noticed in the case of polar and hydrogen bonding solubility parameters, where the lowest values were obtained by using the group contribution method of Hoftyzer and Van Krevelen, δ

_{p}= 2.22 MPa

^{0.5}in δ

_{h}= 7.15 MPa

^{0.5}, and the highest values using the method of Just and Breitkreutz, δ

_{p}= 4.27 MPa

^{0.5}in δ

_{h}= 8.67 MPa

^{0.5}. In the following, the median of all six group contribution methods was considered as the value of the total solubility parameter of ibuprofen.

#### 2.1.2. Polymers and Excipients

**Table 2.**Values of solubility parameters for polymers and excipients by using six different group contribution methods.

Excipient | Method | ||||||
---|---|---|---|---|---|---|---|

Hansen and Beerbower | Fedors | Hoftyzer and Van Krevelen | Hoy | Stefanis and Panayiotou | Just and Breitkreutz | Median δ_{t} (MPa^{0.5}) | |

Copovidone | δ_{t} = 19.01 | δ_{t} = 22.89 | δ_{t} = 24.37 | δ_{t} = 20.25 | δ_{t} = 22.39 | δ_{t} = 21.24 | δ_{t} = 21.82 |

δ_{d} = 19.23 | δ_{d} = 18.18 | δ_{d} = 15.45 | |||||

δ_{p} = 11.15 | δ_{p} = 10.15 | δ_{p} = 8.61 | |||||

δ_{h} = 9.67 | δ_{h} = 7.82 | δ_{h} = 11.42 | |||||

Povidone K30 | δ_{t} = 18.96 | δ_{t} = 23.75 | δ_{t} = 26.28 | δ_{t} = 20.05 | δ_{t} = 23.60 | δ_{t} = 21.75 | δ_{t} = 22.68 |

δ_{d} = 20.44 | δ_{d} = 19.05 | δ_{d} = 16.67 | |||||

δ_{p} = 13.67 | δ_{p} = 12.09 | δ_{p} = 9.85 | |||||

δ_{h} = 9.28 | δ_{h} = 6.86 | δ_{h} = 9.9 | |||||

PEG 6000 | δ_{t} = 18.38 | δ_{t} = 19.17 | δ_{t} = 22.86 | δ_{t} = 21.44 | δ_{t} = 20.45 | δ_{t} = 17.76 | δ_{t} = 19.81 |

δ_{d} = 17.78 | δ_{d} = 17.33 | δ_{d} = 13.6 | |||||

δ_{p} = 11.1 | δ_{p} = 7.93 | δ_{p} = 11.09 | |||||

δ_{h} = 9.13 | δ_{h} = 7.42 | δ_{h} = 2.75 | |||||

Eudragit^{®} E PO | δ_{t} = 17.34 | δ_{t} = 19.59 | δ_{t} = 19.70 | δ_{t} = 18.28 | δ_{t} = 23.51 | δ_{t} = 16.04 | δ_{t} = 19.00 |

δ_{d} = 17.35 | δ_{d} = 16.90 | δ_{d} = 12.19 | |||||

δ_{p} = 3.06 | δ_{p} = 15.45 | δ_{p} = 1.89 | |||||

δ_{h} = 8.81 | δ_{h} = 5.31 | δ_{h} = 10.26 | |||||

Eudragit^{®} S100 | δ_{t} = 20.02 | δ_{t} = 21.86 | δ_{t} = 21.1 | δ_{t} = 19.29 | δ_{t} = 22.37 | δ_{t} = 18.63 | δ_{t} = 20.56 |

δ_{d} = 18.01 | δ_{d} = 16.31 | δ_{d} = 12.18 | |||||

δ_{p} = 3.64 | δ_{p} = 12.3 | δ_{p} = 4.54 | |||||

δ_{h} = 10.38 | δ_{h} = 9.11 | δ_{h} = 13.34 | |||||

Poloxamer 188 | δ_{t} = 18.30 | δ_{t} = 18.81 | δ_{t} = 22.10 | δ_{t} = 20.9 | δ_{t} = 20.33 | δ_{t} = 17.31 | δ_{t} = 19.57 |

δ_{d} = 17.49 | δ_{d} = 17.30 | δ_{d} = 13.66 | |||||

δ_{p} = 10.23 | δ_{p} = 7.72 | δ_{p} = 10.24 | |||||

δ_{h} = 8.74 | δ_{h} = 7.37 | δ_{h} = 2.64 | |||||

Poloxamer 407 | δ_{t} = 18.26 | δ_{t} = 18.64 | δ_{t} = 21.75 | δ_{t} = 20.66 | δ_{t} = 20.28 | δ_{t} = 17.12 | δ_{t} = 19.46 |

δ_{d} = 17.36 | δ_{d} = 17.29 | δ_{d} = 13.68 | |||||

δ_{p} = 9.85 | δ_{p} = 7.63 | δ_{p} = 9.89 | |||||

δ_{h} = 8.57 | δ_{h} = 7.35 | δ_{h} = 2.58 | |||||

Methylcellulose (DS = 1) | δ_{t} = 27.05 | δ_{t} = 29.78 | δ_{t} = 32.29 | δ_{t} = 27.23 | δ_{t} = 24.82 | δ_{t} = 27.45 | δ_{t} = 27.34 |

δ_{d} = 20.73 | δ_{d} = 18.38 | δ_{d} = 17.91 | |||||

δ_{p} = 10.26 | δ_{p} = 7.15 | δ_{p} = 17.74 | |||||

δ_{h} = 22.54 | δ_{h} = 14.82 | δ_{h} = 10.66 | |||||

Ethylcellulose (DS = 3) | δ_{t} = 15.86 | δ_{t} = 18.79 | δ_{t} = 20.18 | δ_{t} = 20.1 | δ_{t} = 19.58 | δ_{t} = 21.42 | δ_{t} = 19.84 |

δ_{d} = 17.59 | δ_{d} = 17.79 | δ_{d} = 16.09 | |||||

δ_{p} = 4.59 | δ_{p} = 6.44 | δ_{p} = 14.05 | |||||

δ_{h} = 8.77 | δ_{h} = 5.05 | δ_{h} = 1.61 | |||||

Xylitol | δ_{t} = 36.86 | δ_{t} = 40.60 | δ_{t} = 41.53 | δ_{t} = 36.60 | δ_{t} = 30.56 | δ_{t} = 31.3 | δ_{t} = 36.73 |

δ_{d} = 20.75 | δ_{d} = 18.62 | δ_{d} = 16.07 | |||||

δ_{p} = 12.68 | δ_{p} = 11.87 | δ_{p} = 21.15 | |||||

δ_{h} = 33.67 | δ_{h} = 21.13 | δ_{h} = 16.54 | |||||

Sucrose | δ_{t} = 35.81 | δ_{t} = 39.95 | δ_{t} = 40.38 | δ_{t} = 33.53 | δ_{t} = 40.83 | δ_{t} = 31.15 | δ_{t} = 37.88 |

δ_{d} = 21.76 | δ_{d} = 21.35 | δ_{d} = 18.55 | |||||

δ_{p} = 9.87 | δ_{p} = 18.44 | δ_{p} = 19.63 | |||||

δ_{h} = 32.55 | δ_{h} = 29.51 | δ_{h} = 15.53 | |||||

Lactose | δ_{t} = 34.07 | δ_{t} = 38.86 | δ_{t} = 40.46 | δ_{t} = 31.48 | δ_{t} = 37.45 | δ_{t} = 38.94 | δ_{t} = 38.16 |

δ_{d} = 22.62 | δ_{d} = 21.78 | δ_{d} = 20.07 | |||||

δ_{p} = 9.63 | δ_{p} = 19.71 | δ_{p} = 27.90 | |||||

δ_{h} = 32.14 | δ_{h} = 23.14 | δ_{h} = 18.30 |

#### 2.2. Experimental Approach

#### 2.2.1. Extended Hansen’s Approach (EHA)

_{χ2}, from the aforementioned procedure were also used in the regression model. By using simple linear regression for the solubility of a given drug, in all solvents, it was not possible to obtain an appropriate calculation procedure for determination of solubility parameters. Also, several types of robust regression, carried out in the statistical program R, gave us results that differ significantly. For this reason, an entirely different approach for processing the experimental data was chosen.

**Figure 1.**ln

_{χ2}as a function of total solubility parameter for (

**a**) ibuprofen; (

**b**) sodium ibuprofen and (

**c**) ibuprofen lysinate.

**Table 3.**Experimental determination of solubility, ln

_{χ2}, for ibuprofen and sodium ibuprofen (data taken from [35]) and ibuprofen lysinate.

Solvent | δ_{t} (MPa^{0.5}) | Ibuprofen | Sodium Ibuprofen | Ibuprofen Lysinate |
---|---|---|---|---|

lnχ_{2} | ||||

Ethanol | 26.52 | −1.9503 | −2.5573 | −8.8013 |

Chloroform | 18.95 | −1.3712 | −7.7910 | / |

Methanol | 29.61 | −3.7017 | −1.3116 | −5.8776 |

Benzene | 18.51 | −2.4684 | −12.3017 | / |

Dioxane | 20.47 | −3.2918 | −8.7174 | −9.8535 |

Acetic acid | 21.37 | −2.1746 | −3.3999 | −3.0117 |

1-Pentanol | 21.93 | −1.5436 | −2.8702 | / |

1-Butanol | 23.20 | / | / | −8.8584 |

1-Propanol | 24.60 | / | / | −9.1191 |

Cyclohexane | 16.80 | −1.8834 | −11.6705 | / |

1,2-Propanediol | 30.22 | −2.4547 | −1.4146 | −3.1307 |

Formamide | 36.65 | −6.5485 | −3.8359 | −4.5675 |

Ethylene glycol | 32.95 | −3.9612 | −0.6762 | −2.9535 |

Glycerol | 36.16 | −5.8932 | −1.2651 | / |

Ethyl acetate | 18.15 | −1.0942 | −7.3852 | −9.6817 |

Propionic acid | 19.95 | −1.5611 | −3.4886 | / |

1-Octanol | 20.56 | −1.5134 | −2.7018 | / |

Heptane | 15.30 | −2.8827 | −11.2964 | −9.1165 |

Chlorobenzene | 19.58 | −3.9057 | −12.9644 | / |

Diethyl ether | 15.64 | −3.8065 | −7.4103 | −11.039 |

Acetone | 19.94 | −1.0474 | −7.8829 | −6.0326 |

Acetophenone | 21.72 | −5.7807 | −10.0583 | / |

N,N-Dimethylformamide | 24.86 | −2.058 | −6.7721 | / |

Dichloromethane | 20.20 | / | / | −9.9672 |

Water | 47.81 | −13.398 | −3.5326 | −3.6882 |

N-Methylformamide | 29.98 | / | −6.2656 | / |

1,4-Butanediol | 33.44 | / | −1.4053 | / |

1,3-Propanediol | 32.65 | / | −2.2121 | / |

Ethylene dichloride | 20.80 | −2.4549 | −10.1933 | / |

Tetrahydrofuran | 23.20 | / | / | 8.5397 |

**Table 4.**The values of solubility parameters for ibuprofen, sodium ibuprofen and ibuprofen lysinat obtained by using EHA.

Drug | Solubility Parameter (MPa^{0.5}) | Analysis Parameters | ||||||
---|---|---|---|---|---|---|---|---|

δ_{t} | δ_{d} | δ_{p} | δ_{h} | No. of Solvents | No. of Combinations | No. of Errors | R^{2} | |

Ibuprofen | 20.56 | 16.60 | 6.91 | 9.97 | 23 | 490,314 | 109,416 | 0.9964 |

Sodium ibuprofenate | 34.12 | 16.38 | 12.52 | 27.19 | 26 | 1,562,275 | 220,884 | 0.9964 |

Ibuprofen lysinate | 31.15 | 16.97 | 22.75 | 12.83 | 16 | 12,870 | 1573 | 0.7594 |

_{d}are highly condensed in a particular area, resulting in greater reliability of estimation of the dispersion solubility parameter. When comparing the histogram of ibuprofen to that of its salts, one can observe an expected shift of values of the polar and hydrogen bonding solubility parameters to higher values. Movements are in line with the increasing hydrophilicity of the ibuprofen molecule after adding lysine and sodium ions.

**Figure 2.**Histograms of most common values of partial solubility parameters obtained by Extended Hansen’s Approach for (

**a**) ibuprofen; (

**b**) sodium ibuprofenate; (

**c**) ibuprofen lysinate; blue color represents values of δ

_{d}, red color represents values of δ

_{p}and green color represents values of δ

_{h}.

#### 2.2.2. Inverse Gas Chromatography (IGC)

**Figure 3.**Graph (δ

^{2}

_{1i})/RT − (χ

^{∞}

_{(1,2)i})/V

_{1}for ibuprofen lysinate as a function of total solubility parameter of solvents, δ

_{1}, at T = 303.15 K; the contribution of δ

_{d}is marked in blue color, δ

_{p}in red color and δ

_{h}in green color.

**Table 5.**Solubility parameters of ibuprofen, taken from [36], and ibuprofen lysinate obtained by using inverse gas chromatography.

Drug | Solubility Parameters | |||
---|---|---|---|---|

δ_{d} | δ_{p} | δ_{h} | δ_{t} | |

Ibuprofen | 12.90 | 6.30 | 12.30 | 18.90 |

Ibuprofen lysinate | 15.74 | 19.18 | 24.92 | 35.17 |

## 3. Discussion of Results

**Table 6.**The values of solubility parameters of ibuprofen and ibuprofen lysinate obtained by the calculation approach and by using experimental methods.

Drug | Method | Solubility Parameters (MPa^{0.5}) | ||||
---|---|---|---|---|---|---|

δ_{d} | δ_{p} | δ_{h} | δ_{t} | |||

Ibuprofen | Group contribution method | |||||

- o
- Median
| 17.56 | 3.22 | 8.31 | 19.71 | ||

Experimental | ||||||

- o
- Extended Hansen’s approach
| 16.60 | 6.91 | 9.97 | 20.56 | ||

- o
- Inverse gas chromatography
| 12.90 | 6.30 | 12.30 | 18.90 | ||

Ibuprofen lysinate | Experimental | |||||

- o
- Extended Hansen’s approach
| 16.97 | 22.75 | 12.83 | 31.15 | ||

- o
- Inverse gas chromatography
| 15.74 | 19.18 | 24.92 | 35.17 |

#### 3.1. Three-Dimensional Evaluation

^{0.5}, indicates potential solubility of a given drug in the tested excipient or polymer.

^{0.5}. The sphere represents the area of solubility of a given drug, where red represents ibuprofen, green ibuprofen lysinate, whose values of solubility parameters were obtained using EHA and blue ibuprofen lysinate, whose solubility parameters value were obtained with the IGC method. In the case that the distance between drug and polymer or excipient was lower than 5 MPa

^{0.5}, the interaction in three-dimensional space is specifically colored.

^{0.5}is obtained by using method developed by Stefanis and Panayiotou (Figure 4b). In this case the solubilization of ibuprofen in PEG 6000, Poloxamer 188, Poloxamer 407 and ethylcellulose can be expected. In general, one can observe that different group contribution methods gave slightly different solubility predictions. For example, when using method of Hoftyzer and Van Krevelen, solubility of ibuprofen in Eudragit E PO, Eudragit S 100 and ethylcellulose is estimated (Figure 4a), and when using the method authored by Just and Breitkreutz, the estimation of solubility is limited only to Eudragit E PO (Figure 4c).

**Figure 4.**The three-dimensional evaluation of solubility parameters taken from Hoftyzer and Van Krevelen; values of partial solubility parameters for excipients and polymers determined using method authored by (

**a**) Hoftyzer and Van Krevelen; (

**b**) Stefanis and Panayiotou and (

**c**) Just and Breitkreutz; The spheres represent the area of solubility of a given drug, where red represents ibuprofen, green ibuprofen lysinate, whose values of solubility parameters were obtained using EHA and blue ibuprofen lysinate, whose values of solubility parameters were obtained with the IGC method. EC—ethylcellulose; L—lactose; MC—methylcellulose; S—sucrose; X—xylitol; Eudragit E PO, P (188, 407) Poloxamers.

#### 3.2. Two-Dimensional Evaluation

^{0.5}represents the range of solubility. Bagley’s diagrams in Figure 5 differ according to the group contribution method choice used in determination of solubility parameters of polymers and excipients. Polymers and excipients are marked as grey circles, while ibuprofen is presented as a red ellipse, ibuprofen lysinate, whose values of solubility parameters were obtained using EHA, is presented as a green ellipse and ibuprofen lysinate, whose values of solubility parameters were obtained by using the IGC method, is presented as a blue ellipse.

**Figure 5.**Bagley’s plot; values of solubility parameters of polymers and excipients according to (

**a**) Hoftyzer and Van Krevelen; (

**b**) Stefanis and Panayiotou and (

**c**) Just and Breitkreutz; polymers and excipients are marked as grey circles, while ibuprofen is presented as a red ellipse, ibuprofen lysinate, whose values of solubility parameters were obtained using EHA, is presented as a green ellipse and ibuprofen lysinate, whose values of solubility parameters were obtained by using the IGC method, is presented as a blue ellipse. MC—methylcellulose; S—sucrose; X—xylitol.

^{0.5}is calculated only for xylitol, sucrose and methylcellulose (Figure 5c).

#### 3.3. One-Dimensional Evaluation

^{0.5}in regards of solubility. Figure 6 illustrates a bar graph of the absolute difference between solubility parameters of ibuprofen and selected polymers and excipients. According to Greenhalgh’s approach, solubility of ibuprofen was predicted in the majority of selected substances, with the exception of lactose, sucrose, xylitol and methylcellulose.

_{t}, was calculated with methylcellulose. The value is Δδ

_{t}= 3.81 MPa

^{0.5}. In the case of using IGC method for determination of solubility parameters (Figure 8), the lowest difference in the total solubility parameter, Δδ

_{t}, was calculated with xylitol. The value is Δδ

_{t}= 1.56 MPa

^{0.5}.

**Figure 7.**Bar graph according to Greenhalgh for ibuprofen lysinate; solubility parameters of ibuprofen lysinate were obtained using EHA.

**Figure 8.**Bar graph according to Greenhalgh for ibuprofen lysinate; solubility parameters of ibuprofen lysinate were obtained using IGC.

## 4. Materials and Methods

#### 4.1. Materials

#### 4.2. Methods

#### 4.2.1. Calculation Methods

#### Group Contribution Methods (GCM)

_{t}, directly, whilst other three group contribution methods, authored by Hoftyzer and Van Krevelen, Stefanis and Panayiotou and Just and Breitkreutz, gave the values of partial solubility parameters. The total solubility parameter, δ

_{t}, is calculated using Equation (3), if needed. An example of calculation of solubility parameters for a drug ibuprofen and a polymer polyvinylpyrrolidone, using one of the group contribution methods, is shown in Table 7 and Table 8, respectively.

**Table 7.**Calculation of solubility parameters for the drug ibuprofen, using the group contribution method of Hoftyzer and Van Krevelen.

Individual Functional Group | Frequency | F_{di} (MJ/m^{3})^{0.5}·mol^{−1} | F_{pi}^{2} (MJ/m^{3})^{0.5}·mol^{−1} | E_{hi} (J/mol) | V_{m} (cm^{3}/mol) | |
---|---|---|---|---|---|---|

–CH_{3} | 3 | 420 × 3 | 0 | 0 | 33.5 × 3 | |

>CH– | 2 | 80 × 2 | 0 | 0 | −1.0 × 2 | |

–CH_{2}– | 1 | 270 | 0 | 0 | 16.1 | |

phenylene (p) | 1 | 1270 | 110^{2} | 0 | 52.4 | |

–COOH | 1 | 530 | 420^{2} | 10,000 | 28.5 | |

Sum | - | 3490 | 188,500 | 10,000 | 195.5 | |

Calculations and results | ${\mathsf{\delta}}_{d}=\frac{\sum {F}_{di}}{{V}_{m}}$ | δ_{d} = 17.85 | ||||

${\mathsf{\delta}}_{p}=\frac{\sqrt{\sum {F}_{pi}^{2}}}{{V}_{m}}$ | δ_{p} = 2.22 | |||||

${\mathsf{\delta}}_{h}=\sqrt{\frac{\sum {E}_{hi}}{{V}_{m}}}$ | δ_{h} = 7.15 | |||||

${\mathsf{\delta}}_{t}^{2}={\mathsf{\delta}}_{d}^{2}+{\mathsf{\delta}}_{p}^{2}+{\mathsf{\delta}}_{h}^{2}$ | δ_{t} = 19.36 |

**Table 8.**Calculation of solubility parameters for the polymer polyvinylpyrrolidone, using the group contribution method of Hoftyzer and Van Krevelen.

Individual Functional Group | Frequency | F_{di} (MJ/m^{3})^{0.5}·mol^{−1} | F_{pi}^{2} (MJ/m^{3})^{0.5}·mol^{−1} | E_{hi} (J/mol) | V_{m} (cm^{3}/mol) | |
---|---|---|---|---|---|---|

–CH_{2}– | 4 | 270 × 4 | 0 | 0 | 16.1 × 4 | |

>CH– | 1 | 80 | 0 | 0 | −1.0 | |

–N< | 1 | 20 | 800^{2} | 5000 | −9.0 | |

>C=O | 1 | 290 | 770^{2} | 2000 | 10.8 | |

ring (5) | 1 | 190 | - | - | 16.0 | |

Sum | - | 1660 | 1,232,900 | 7000 | 81.2 | |

Calculations and results | ${\mathsf{\delta}}_{d}=\frac{\sum {F}_{di}}{{V}_{m}}$ | δ_{d} = 20.44 | ||||

${\mathsf{\delta}}_{p}=\frac{\sqrt{\sum {F}_{pi}^{2}}}{{V}_{m}}$ | δ_{p} = 13.67 | |||||

${\mathsf{\delta}}_{h}=\sqrt{\frac{\sum {E}_{hi}}{{V}_{m}}}$ | δ_{h} = 9.28 | |||||

${\mathsf{\delta}}_{t}^{2}={\delta}_{d}^{2}+{\delta}_{p}^{2}+{\delta}_{h}^{2}$ | δ_{t} = 26.28 |

#### 4.2.2. Experimental Approach

#### Extended Hansen Approach (EHA)

#### Inverse Gas Chromatography (IGC)

## 5. Conclusions

_{t}, did not differ significantly among methods, whereas, the values of partial solubility parameters deviated. The largest deviation was estimated in the case of the polar, δ

_{p}, and hydrogen bonding, δ

_{h}, solubility parameters. Since the line between both of the aforementioned solubility parameters is rather thin, the better selection and greater number of solvents, used in EHA and IGC, could give us smaller deviations and more reliable data. Due to the simpler nature and structure of the ibuprofen molecule, we were able to use a calculation approach in order to obtain solubility parameter values. The calculation results were in good agreement when compared to experimental data, regarding all three solubility parameters. The interpretation of these results was nevertheless rather challenging, due to the complex behavior of salts in the presence of solvents. The existence of reliable models for salts, on which one could rely, is negligible so far.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Sample Availability**: Samples of the compounds are not available from the authors.

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**MDPI and ACS Style**

Kitak, T.; Dumičić, A.; Planinšek, O.; Šibanc, R.; Srčič, S. Determination of Solubility Parameters of Ibuprofen and Ibuprofen Lysinate. *Molecules* **2015**, *20*, 21549-21568.
https://doi.org/10.3390/molecules201219777

**AMA Style**

Kitak T, Dumičić A, Planinšek O, Šibanc R, Srčič S. Determination of Solubility Parameters of Ibuprofen and Ibuprofen Lysinate. *Molecules*. 2015; 20(12):21549-21568.
https://doi.org/10.3390/molecules201219777

**Chicago/Turabian Style**

Kitak, Teja, Aleksandra Dumičić, Odon Planinšek, Rok Šibanc, and Stanko Srčič. 2015. "Determination of Solubility Parameters of Ibuprofen and Ibuprofen Lysinate" *Molecules* 20, no. 12: 21549-21568.
https://doi.org/10.3390/molecules201219777