Direct fluorination of tetrafluoroethylene at low temperatures

Journal Pre-proof Direct Fluorination of Tetrafluoroethylene at Low Temperatures Matthew P. Confer, Sadulla R. Allayarov, Ida P. Kim, I.V. Markin, Virgil E. Jackson, David A. Dixon

PII:

S0022-1139(20)30044-0

DOI:

https://doi.org/10.1016/j.jfluchem.2020.109493

Reference:

FLUOR 109493

To appear in:

Journal of Fluorine Chemistry

Received Date:

20 December 2019

Revised Date:

12 February 2020

Accepted Date:

12 February 2020

Please cite this article as: Confer MP, Allayarov SR, Kim IP, Markin IV, Jackson VE, Dixon DA, Direct Fluorination of Tetrafluoroethylene at Low Temperatures, Journal of Fluorine Chemistry (2020), doi: https://doi.org/10.1016/j.jfluchem.2020.109493

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.

Direct Fluorination of Tetrafluoroethylene at Low Temperatures Matthew P. Confer

a,b

, Sadulla R. Allayarov a,c, Ida P. Kim c, I.V. Markin d, Virgil E. Jackson a,

and David A. Dixon a* a

Department of Chemistry and Biochemistry, The University of Alabama, Shelby Hall, Box

870336, Tuscaloosa, Alabama, USA, 35487-0336 E-mail: [email protected] Phone: 205-348-8441 Department of Chemical and Biological Engineering, The University of Alabama, Tuscaloosa,

of

b

c

ro

AL 35487, USA

Institute of Problems of Chemical Physics of the Russian Academy of Sciences, Chernogolovka,

Perm Branch of Federal State Unitary Enterprise “Russian Scientific Center “Applied

re

d

-p

the Moscow Region, Russia, 142432

ur na

Graphical abstract

lP

Chemistry”” Perm, Russia, 614034

F

C2F6 :CF2

3

CF4

Jo

C 2F 6 C 3F 8

CF

Highlights

1



Reaction of F2 with TFE in hexafluoropropene (HFP) dimer and trimer matrices leads to C 2F6 without explosions.



(HFP)2 and (HFP)3 moderate the chain branching fluorination of TFE by trapping F atoms in long-lived radicals.



High level composite correlated molecular orbital theory G3(MP2) calculations used to



of

develop mechanism. Equilibrium products of TFE direct fluorination e determined by gas phase Gibbs free energy

Approximate local temperature where reactions occur predicted.

-p



ro

minimization.

re

Abstract

Mechanisms for the processes of direct fluorination of tetrafluoroethylene (TFE) in matrices of

lP

TFE, hexafluoropropylene (HFP), and dimers and trimers of HFP ((HFP) 2 and (HFP)3) from 77 K to 300 K have been developed. Electronic structure calculations at the composite correlated

ur na

G3(MP2) and G4 molecular orbital theory levels of the energetics of a range of reactions involving TFE and fluorine are presented to aid in the development of these mechanisms. The equilibrium products of the direct fluorination of TFE in the gas phase at varied temperature and initial composition was determined by Gibbs free energy minimization. Spontaneous reactions

Jo

(explosions) were observed for the fluorination of pure crystalline TFE and HFP. Fluorination of TFE can be performed without explosion in glassy matrixes of (HFP) 2 or (HFP)3 at low temperatures. The explosive nature of the reaction decreases in the matrix order TFE > (HFP) 2 > (HFP)3. The fluorination of TFE begins at the phase transition temperature of the matrix, i.e., after the transition of devitrified (HFP)2 and (HPF)3 into the supercooled liquid state at 110 K and 150

2

K, respectively. The experiments show that either the presence of a branched structure (C 9F20, the saturated analog of (HFP)3) or the presence of unsaturated bonds (perfluorotoluene) separately cannot provide a medium for the safe fluorination of TFE as the direct fluorination of TFE in these matrices led to an explosion. HFP oligomers provide an effective environment for TFE fluorination because of the presence of double bonds surrounded by the branched perfluorinated groups. The unsaturated bonds of the HFP oligomers are an active participant in the chemical processes

ro

of

involved in the safe, direct fluorination of TFE.

Keywords: tetrafluoroethylene; dimer and trimer of hexafluoropropylene; vitrified matrixes;

-p

fluorination mechanism; long–lived radicals; composite correlated molecular orbital theory.

re

1. Introduction

There is a broad technology base for the synthesis of organofluorine compounds [].

lP

Whatever strategy is adopted for the preparation of a particular target molecule, whether it is a biologically active derivative for the life science industry [], an organic or inorganic material [], or

ur na

synthesizing or modifying a high molecular weight polymer for the materials sector [], the key step is the synthesis of a C-F bond at some stage in the synthetic sequence. Many fluorinating agents, with varying degrees of success, have been developed over the years with the goal of solving this fundamental synthesis problem [].

Jo

Elemental fluorine is a viable reagent for synthesis of C-F bonds for a range of organic

systems. The direct fluorination of organic compounds with F2 as the reagent is not straightforward, as controlling any reaction with elemental fluorine and dealing with the heat release can lead to complications [30]. The reaction between an organic compound and molecular fluorine is usually highly exothermic [1-,2,3,5,16], so careful temperature control is required to

3

avoid burning and explosions and to achieve reproducible results. As a result, molecular fluorine is most often used in a dilute form with concentrations < 50 vol% in an inert gas such as N 2 or Ar. In industry, alternative methods of fluorination rather than direct fluorination using elemental fluorine are usually practiced [1,5,31]. As an example, fullerenes can react with molecular fluorine with the formation of radicals at liquid nitrogen temperature (77 K) [32].

The degree of

fluorination of carbon nanotubes depends on the method of fluorination and on the chemical

of

composition of the nanotubes [33] with the highest degree of fluorination observed for pre-

ro

oxidized nanotubes.

Direct fluorination of materials has a number of potentially useful features. This process

-p

occurs spontaneously, i.e., it does not require heating, initiation, or the presence of catalysts.

re

Although energy may not need to be input for the process to occur, energy will be needed for cooling purposes to manage the reaction exothermicity. It enables the use of widely available and

lP

cheap organic compounds or polymers as the reactant, while avoiding the costly synthesis of fluorine containing organic compounds and polymers as starting materials. Another feature of

ur na

direct fluorination is the "dry" technology for surface modification of polymers, which does not substantially affect the chemical and physical structure of the polymer in the bulk but does improve the operational characteristics of the surface of polymers for applications such as gas separation, barrier properties, and adhesion. Despite the attractive features of direct fluorination, it has only

Jo

been used on the industrial scale for a few applications [] including the improvement of the adhesive properties of polymeric materials []. Safety is an important issue with direct fluorination at industrial scales. A characteristic of the direct fluorination of organic compounds is the high content of fluorinated alkanes with low molecular weight in the composition of the products, in contrast of

4

the relatively low yield (a few percent) of the perfluorinated analogues of the initial organic reagent. This may be due in part to the bond energy of the C-F bond (120 - 130 kcal/mol) being substantially larger than the C–H bonds (95 - 105 kcal/mol) they are replacing [42]. The energy released can lead to breaking C-C bonds and degradation of the organic compound. In addition, the relatively low energy of dissociation of the F–F bond (37.4 kcal/mol) [42] can contribute to branching in the chain fluorination process and, in the case of inadequate heat dissipation, can lead

of

to an explosion [36,43,44]. The rate of the reaction may be reduced by the substitution of hydrogen

ro

atoms with fluorine atoms in the organic compounds [45], which enables fluorination of the partially fluorinated organic compound to achieve a fairly high yield of the perfluorinated analog

-p

[46].

re

In the gas phase, the controlled fluorination of organic molecules, such as tetrafluoroethylene (TFE), can be only be carried out in an inert environment to minimize

lP

explosions due to chain branching. Energetic chain branching occurs due to decomposition of the primary excited products of fluorination, which are formed by formation of C-F bonds. These

ur na

products can decompose into several active particles able to initiate the chain process [47]. The elementary stages of the energetic chain branching of the fluorination of hydrocarbons are shown in the following scheme:

(1)

R• + F2 → RF* + F•

(2)

RF* → R•1 + R•2

(3)

Jo

F + RH → HF + R•

where, R is an alkyl radical, hydrogen, deuterium, etc. The amount of heat released from the second reaction depends on a structure of the radical (R•). The excited molecules RF* decompose by initiating the chain branching process (reaction (3)). For gas phase fluorination, all of the energy

5

of addition of fluorine to the double bond of TFE may be in the vibrational energy of the formed perfluoroethyl radical leading to radical decomposition: (F3CCF2)*→ CF3 + :CF2

(4)

This reaction is endothermic by 54.6 kcal/mol using the values obtained below. The inert environment molecules can deactivate excited molecules or radicals via collisions with them. Such

of

deactivation can occur also by transfer of the excitation energy to the surface of the reaction vessel. The direct fluorination of organic compounds in a liquid environment [48-,49,52,51,52]

ro

may also proceed on the interface between the liquid and gas phases or in gas bubbles. Therefore, the reaction medium will not be completely homogeneous and additional efforts are required to

-p

overcome the potential for an explosion. It has been proposed [] that the use of branched

re

perfluoroalkenes, particularly oligomers of hexafluoropropene (HFP) [58], can serve as an environment for safe liquid-phase direct fluorination. Direct fluorination processes can be carried

lP

out without explosion and result in high yields of the products formed upon addition of fluorine to the unsaturated bonds. However, processes occurring under warming of the reaction medium have

ur na

not been studied. Such processes must be understood prior to use of HFP oligomers as a diluent in direct fluorination reactions of TFE in either low temperature solid phase or in liquid phase. Direct fluorination of TFE may proceed through several mechanisms dependent upon reaction conditions. A universal mechanism for direct fluorination of TFE has not been determined

Jo

due to the highly condition dependent nature of the mechanism. Based on available data, three mechanisms for the reactions between fluorine and TFE can be proposed: Molecular addition: F2C=CF2 + F2  C2F6

(5)

Chain addition:

6

F2C=CF2 + F  F3CCF2

(6)

F3CCF2 +F2  C2F6 + F

(7)

Carbene formation: F2C=CF2 + F  CF3 + :CF2

(8)

:CF2 + F2  CF4

(9)

CF3 + F2  CF4 + F

(10)

of



The available data on the low temperature direct fluorination of perfluoroolefins [] and

ro

polymers [62,63] does not allow for a conclusive determination of the mechanism of the

-p

spontaneous generation of radicals, and the results are sometimes contradictory. Mechanisms involving simultaneous reactions and the transformation of molecular complexes have been

re

proposed to explain [64] the process of initiating the spontaneous direct fluorination of polymers [63,65] and perfluoroolefins [20,53,59-,60,61]. In addition, there is no data on the influence on the

lP

fluorination process of the properties and the physical state of matrix used in solid-phase fluorination. For example, the nature of nucleation of active centers able to initiate low temperature

ur na

fluorination has not been elucidated. To address these issues, experimental studies of the low temperature direct fluorination of tetrafluoroethylene (TFE) in solid phase perfluorinated organic environments were performed in combination with quantum chemical electronic structure.

Jo

2. Results and Discussion

2.1 Calculated Reaction Energies for Direct Fluorination Processes Although there is a range of data available for the heats of various fluorocarbons and radicals [42,66] we have calculated these values at the G3(MP2) [67] and G4 [68] levels to provide a consistent set of results. As shown in Table 1, the G3(MP2) and G4 results are in good agreement with each other and with the best available results which represent a combination of values from experiment [66], G3(MP2),

7

and higher level electronic structure calculations [69,70]. The density functional theory results with the B3LYP [71,72] functional with the DZVP2 basis set [73] is not in as good agreement with the best values as are the composite correlated molecular orbital theory results. Reactions (35)(79) were only calculated at the B3LYP/DZVP2 level due to the high computational cost of the large, open shell, molecules making G3(MP2) and G4 methods too expensive. Corrections to

Jo

ur na

lP

re

-p

ro

of

reaction enthalpies from B3LYP/DZVP2 were applied to reactions (35, 36-41, 48-58, 61, 63-65,

8

Table 1. Reaction enthalpies at 298 K in kcal/mol of the reactions between tetrafluoroethylene and fluorine.

12

CF2=CF2 + F2 → :CF2 + CF4

13

CF2=CF2 + F2 → 2 CF3

14

CF2=CF2 + F2 → CF3CF2 + F

15

:CF2 + F2 → CF3 + F

16

F+ CF2=CF2 → CF3CF2

17

F2C=CF2 + F → CF3 + :CF2

18

:CF2 + F→ CF3 

СF3 + F2 → CF4 + F

lP

19

G4

B3LYP

Besta

-160.6

-160.7

-147.2

-160.5

-108.4

-108.9

-95.2

-108.6

-62.3

-64.8

-59.4

-63.4

-34.7

-36.9

-31.5

-33.3

-46.0

-47.4

-46.4

-46.7

-72.5

-74.7

-69.3

-71.3

-16.3

-17.4

-13.0

-16.7

-83.8

-85.2

-84.2

-84.7

-92.2

-91.4

-82.3

-91.9

-88.1

-86.1

-77.9

-89.2

of

CF2=CF2 + F2 → C2F6

G3(MP2)

ro

11

-p

Reactions

re

No.

CF3CF2 + F2 → C2F6 + F

21

CF2=CF2 + СF3→ СF3СF2СF2

-42.4

-44.0

-37.9

-43.2

22

CF2=CF2 + СF3→ СF3СFСF3

-48.7

-50.7

-44.1

-49.5

ur na

20





СF3СF2С F2 + F → С3F8

-124.9

-121.6

-114.3

-124.9

24

СF3СF2СF2 + F2 → С3F8 + F

-88.4

-84.6

-80.9

-86.9

25

СF3СFСF3 + F → С3F8

-118.5

-115.0

-108.0

-118.6

26

СF3СFСF3 + F2 → С3F8 + F

-82.0

-78.0

-74.6

-80.6

27

CF3-CF2+ CF2=CF2 → CF3CF2CF2CF2

-38.8

-40.3

-32.5

-41.9

CF3CF2 + F → C2F6

-125.9

-123.9

-115.7

-127.2

CF2=CF2 + :CF2 → CF3CF=CF2

-67.3

-67.4

-65.7

-68.9

CF3CF2 + CF3CF2 → C4F10

-91.0

-86.1

-77.2

-95.4

31

CF2=CF2 + :CF2 → c-С3F6

-37.3

-37.5

-38.8

-38.9

32



-120.1

-130.2

-129.2

-129.9

28 29 30

Jo

23

СF3 + F → CF4 9

F+ F → F2

33

CF3CF2 + CF3CF2 → CF2=CF2 + C2F6

35

CF2=CF2 + C2F5C•F2 → CF3(CF2)3CF2

36b

A

b

A

38

b

A

39

(CF3)2CFCF2CFCF3 → (CF3)2CFCFCF2 + CF3

40b,d

A

41b,d

A

42b

A

b

A

44

b,c

A

45b

B

46b

B

b

B

48

b

B

49b

B

50b 51d

47

52 53 54



-37.8

-37.9

-53.4

-49.2

-46.4

-55.9

-30.6

-36.7

ro

(HFP)2 + F → (CF3)2CFCFCF2CF3 

(HFP)2 + CF3→ (CF3)2CFCFCF(CF3)2

re

(HFP)2 + CF3CF2 → (CF3)2CFCFCF(CF3)(C2F5)

-p

(HFP)2 + F → (CF3)2CFCF2C FCF3

-119.7 -56.2

-61.6

-53.2

-58.6

27.5

33.6

-26.8

-32.9

-18.9

-26.7

-18.4

(HFP)2 + F2 → (CF3)2CFCF2CFCF3 + F

-15.4

(HFP)3 + F2 → (CF3)2CFCF(C2 F5)CF(CF3)2

-95.1

(HFP)2 + F2 → (CF3)2CF(CF2)2CF3

-114.9

(HFP)2 + F2 → (CF3)2C(CF2)2CF3 + F

-13.6

(HFP)2 + F2 → (CF3)2CFCFCF2CF3 + F

-13.7

(HFP)2 + F → (CF3)2C(CF2)2CF3

-47.0

-52.4

(HFP)2 + F → (CF3)2CFCFCF2CF3

-47.1

-52.5

(CF3)2C(CF2)2CF3 → CF3CF=CFCF2CF3 + CF3

26.5

32.6

(CF3)2CFC(C2F5)CF(CF3)2 + F → (CF3)2CFCF(C2F5)CF(CF3)2

-79.3

-87.5

(CF3)2CFCF(C2F5)C(CF3)2 + CF3CF2→ A(HFP)3 + C2F6

-68.4

-76.6

(CF3)2CFC(C2F5)CF(CF3)2 + CF3CF2→ A(HFP)3 + C2F6

-67.1

-75.3

(CF3)2CFC(C2F5)CF(CF3)2 + CF3 → (HFP)3 + CF4

-66.5

-74.7

(HFP)3 + F → (CF3)2CFC(C2F5)CF(CF3)2

-53.6

-59.0

(HFP)3 + F → (CF3)2CFCF(C2F5)C(CF3)2

-47.2

-55.4

lP

(HFP)2 + F2 → (CF3)2CFCFCF2CF3 + F

ur na

43

(HFP)2 + F2 → (CF3)2CF(CF2)2CF3

Jo

37

-37.8

of

34

-37.8

55c

A

56c,d

A

A

10

(CF3)2CFC(CF3)(C2F5)C(CF3)2 → (CF3)2CFC(C2F5)CFCF3 + CF3

11.4

17.5

58

(CF3)2CFC(CF3)(C2F5)C(CF3)2 → (CF3)2CFCF(C2F5)CFCF2 + CF3

34.0

40.1

59

(CF3)2CFC(C2F5)CF(CF3)2 + F2 → (CF3)2CFCF(C2F5)CF(CF3)2 + F

60c

A

61

(CF3)2CFC(C2F5)CF(CF3)2 + CF2=CF2 → A(HFP)3 + CF3CF2 A

63

c,d

B

64c,d

A

65c,d

A

66c

B

67c

B

68

B

69

B

70

[(CF3)2CF]2CFCFCF3 → [(CF3)2CF]2CCF2 + CF3

71c

C

72c

C

73c

C

74

c

C

75c

C

77 78 79

(HFP)3 + CF3 →(CF3)2CFC(C2F5)C(CF3)3

(HFP)3 + F2 →[(CF3)2CF]2CC2 F5 + F

re

(HFP)3 + CF3 → (CF3)2CFC(CF3)(C2F5)C(CF3)2

-41.5 -15.8 -15.8

-23.6

-9.4 -7.5

-13.6

-3.7

-9.8

-1.4

-7.5

-13.3 2.6

(HFP)3 + F →[(CF3)2CF]2CC2 F5

-46.7

-52.1

(HFP)3 + F → [(CF3)2CF]2CFCFCF3

-30.8

-36.2

3.5

9.6

ur na

lP

(HFP)3 + F2 → [(CF3)2CF]2CFCFCF3 + F

(HFP)3 + F2 → (CF3)2CFCF2CF(CF3)(CF2)2CF3

-108.2

(HFP)3 + F2 → (CF3)2CFCFCF(CF3)(CF2)2CF3 + F

-11.7

(HFP)3 + F2 → (CF3)2CFCF2C (CF3)(CF2)2CF3 + F

-14.1

(HFP)3 + F → (CF3)2CFCFCF(CF3)(CF2)2CF3

-45.1

-50.5

(HFP)3 + F → (CF3)2CFCF2C (CF3)(CF2)2CF3

-47.5

-52.9

(CF3)2CFCFCF(CF3)(CF2)2CF3 → (CF3)2CFCF=CF(CF2)2CF3 + CF3

19.0

25.1

(CF3)2CFCFCF(CF3)(CF2)2CF3 → CF3CF=CFCF(CF3)(CF2)2CF3 + CF3

23.8

29.9

(CF3)2CFCF2C(CF3)(CF2)2CF3 → (CF3)2CFCF2CF=CFCF2CF3 + CF3

26.0

32.1

(CF3)2CFCF2C(CF3)(CF2)2CF3 → (CF3)2CFCF=CF(CF2)2CF3 + CF3

21.5

27.6

Jo

76

(HFP)3 + CF3 →[(CF3)2CF]3C

-p

(HFP)3 + F2 → (CF3)2CFCF(C2 F5)C(CF3)2 + F

c

62

ro

(HFP)3+ F2 → (CF3)2CFC(C2 F5)CF(CF3)2 + F

of

57

11

These results are obtained using heats of formation for C2F6, CF4, CF3CF2, F, and F2 from [66], for C2F4 from [69], for :CF2, CF3 from [70], and for СF3СF2СF2, СF3СFСF3, C3F8, CF3CF2CF2CF2, CF3CF=CF2, C4F10, and C3 F6 cyclic from this work for reactions (11-34) and corrected B3LYP values from [74] for reactions (35-79). b A(HFP)2 - isomer (CF3)2CFCF=CFCF3 of (HFP)2 and B(HFP)2 isomer (CF3)2C=CFCF2CF3 of (HFP)2. c A(HFP)3 - isomer (CF3)2CFC(C2F5)=C(CF3)2 of (HFP)3, B(HFP)3 - isomer [(CF3)2CF] 2C=CFCF3 of (HFP)3, and C(HFP)3 - isomer (CF3)2CFCF=C(CF3)(CF2)2CF3 of (HFP)3. d Values from [74]

Jo

ur na

lP

re

-p

ro

of

a

12

68-70, and 74-79) based upon [74]. Corrections from the following reactions were used: C2F4 + CF3 → CF3CF2C•F2 (6.1 kcal/mol) for reactions (35, 39, 40, 50, 57, 58, 63-65, 70, and 76-79);



C2F5• + F• → C2F6 (8.2 kcal/mol) for reactions (51-54, and 56); C2F4 + F• → CF3C•F2 (5.4 kcal/mol) for reactions (37, 38, 48, 49, 55, 68, 69, 74, and 75); and C 2F4 + C2F5• → CF3CF2CF2CF2• (7.8 kcal/mol) for reaction (41, and 61) [74].

of

2.2 TFE Gas Phase Direct Fluorination Thermodynamics Heats of formation and calculated entropies (Table S4) were used to predict the gas phase free energies for species involved in the

ro

direct fluorination of TFE. A Gibbs free energy minimization approach can be used to predict the

-p

equilibrium variation in species as a function of the temperature [75]. The Gibbs free energy minimization was performed between 250 K and 4000 K to determine equilibrium product

re

amounts for a gas phase mixture of TFE, C2F6, F2, :CF2, CF4, CF3, CF3CF2, F, CF2CF2CF3,

lP

CF3CFCF3, C3F8. The gas phase mixture was assumed to be ideal and at 1 bar. The system was subject to multiple mole balances ranging from 2C:6F to 2C:12F as shown in Figure 1. Both temperature independent and temperature dependent enthalpy and entropy terms were used for

ur na

Gibbs free energy minimization, Figure S1 and Table S5 and S6. No significant differences in the curves were found between use of temperature independent or temperature dependent enthalpy and entropy terms, so only temperature independent figures are presented in Figure 1.

Jo

At low C:F ratios, Figure 1a-c, CF4, C2F6, and C3F8 are present at low temperatures (below ~1500 K), TFE is an equilibrium product between ~800K and 2000 K, and :CF2 and F dominate the product composition as temperature increases to 4000 K. At high C:F ratios, Figure 1d-g, CF4 is the dominant low temperature product with F2 and F forming in the highest C:F ratio mixtures. The dominant high temperature products are :CF2 and F at high C:F ratios. No C2F6 or C3F8 is predicted to form at any temperature for high C:F ratios. Gibbs free energy minimization 13

of ro -p re lP ur na Jo Figure 1. Equilibrium amounts (mol) of product with respect to temperature by Gibbs free energy minimization with mole ratio a. 2C:6F b. 3C:8F c. 3C:10F d. 2C:8F e. 3C:14F f. 2C:10F g. 2C:12F. 14

demonstrates that low temperatures (less than ~750 K) and low C:F ratios should be used to maximize C2F6 production and minimize side products at equilibrium. The formation of C2F6 when there is a 1:1 ratio of F2:C2F4 is consistent with experiment at low temperatures in the presence of HFP oligomers [76]. The modeling results help to provide insights into the effective local temperature of the reactant mixture. In solid or liquid HFP, the effective local temperatures in a reacting zone are likely to be

of

less than 800 K based upon Figure 1. The crossing point for CF4 and C2F6 of ~ 1000 K in Figure

ro

1 suggests that this is the effective local temperatures in the reacting zone in the perfluoroaromatics solvents. The effective temperature in the straight chain perfluoroalkane solvents is around 1500

-p

K. CF3 radicals do not appear at low temperatures for any C:F ratio but are likely present prior to

re

equilibrium is reached because carbon must be added to the initial TFE in order to produce the C3F8 present at equilibrium. As temperature increases the total moles of gas in the system

lP

increases, Figure S2. The increase in total moles of gas is due to the entropy term in Equation (83) dominating at high temperatures.

ur na

Experimental: Fluorination of TFE in Solid Matrices The reactivity of TFE with F2 was studied by fluorination of pure TFE and solid vitrified solutions of TFE in hexafluoropropylene oligomers, (HFP)2 and (HFP)3 [76Error! Bookmark not defined.]. The form of the physical structure of frozen perfluoroolefins depends on their physical structure and the mode of freezing. Table 2

Jo

contains phase change temperatures for the pure components of TFE, F2, HFP, (HFP)2, and (HFP)3. The influence of TFE concentration on mixtures of (HFP)2 and TFE was determined for

solid solutions [76]. At concentrations greater than 20 mol% TFE, the solid is a mixture of crystalline TFE and glassy (HFP)2. The phase transitions of TFE-(HFP)2 mixtures with TFE concentration greater than 20 mol% are essentially the same as the phase transitions for pure TFE

15

and (HFP)2. Samples containing less than 20 mol% TFE demonstrate the same processes, except for melting of TFE. TFE-(HFP)2 mixtures with TFE concentration less than 20 mol% TFE form transparent homogenous glassy solutions at 77 K. The warming curves show devitrification of glassy (HFP)2, crystallization of (HFP)2, and melting of (HFP)2; melting of TFE is not observed. TFE does not form its own crystalline phase and is fully dissolved in a vitrified matrix of (HFP) 2. TFE does not form a crystalline phase upon warming to 300 K. The amount of crystalline TFE in

of

the solid solution of TFE in (HFP)2 at 77 K is less than 1%. The initial mixtures of TFE and (HFP) 2

ro

need to be cooled slowly (60 K/min) during freezing to 77 K to obtain a fully glassy solution. If

re

and the solution will not be homogenous at 77 K.

-p

the TFE-(HFP)2 mixture is cooled too quickly some or all of the TFE can form a crystalline phase

Table 2. Phase change temperatures (T, K) for pure components in TFE fluorination reactions

lP

[76,77]. Values in parentheses are calculated at the DFT level.

Jo

ur na

Material Phase Change T TFE Crystal → Liquid 142 TFE Liquid → Gas 197(178) F2 Liquid → Gas 85(78) HFP Crystal → Liquid 115 HFP Liquid → Gas 244(238) (HFP)2 Glass → Supercooled Liquid 110 (HFP)2 Supercooled Liquid → Crystal 124 (HFP)2 Crystal → Liquid 176 (HFP)2 Liquid → Gas ((A)350/(B)357)a (HFP)3 Glass → Supercooled Liquid 150 (HFP)3 Liquid → Gas ((A)428/(B)436/(C)462)b a A (HFP)2 - isomer (CF3)2CFCF=CFCF3 of (HFP)2 and B(HFP)2 - isomer (CF3)2C=CFCF2CF3 of (HFP)2. b A(HFP)3 - isomer (CF3)2CFC(C2F5)=C(CF3)2 of (HFP)3, B(HFP)3 - isomer [(CF3)2CF] C 2C=CFCF3 of (HFP)3, and (HFP)3 - isomer (CF3)2CFCF=C(CF3)(CF2)2CF3 of (HFP)3. The influence of TFE concentration in the initial mixture on the phase state of the solid solution at 77 K was examined with (HFP)3 as the solvent [76]. At concentrations of TFE greater

16

than 60 mol%, solid mixtures of crystalline TFE and glassy (HFP)3 formed. A fully glassy matrix without any crystalline TFE is formed for mixtures with less than 60 mol% TFE in (HFP) 3. For TFE concentrations less than 60 mol% the calorimetric curves of warming TFE-(HFP)3 mixtures are fully analogous to the warming curves of pure (HFP) 3 with no melting of TFE observed. Characteristic heat release with respect to temperature for TFE/F2, HFP/F2, (HFP)2/F2, and (HFP)3/F2 mixtures are presented in Table 3. Explosions at 85 K with TFE and HFP cannot be a

of

result of olefin molecules moving due to phase transformations as both olefins are in the crystalline

ro

state. If the organofluorine molecules are in motion, there should be differences in explosion temperatures as HFP has a lower melting temperature (115 K) than TFE (142 K) with

-p

corresponding heats of melting of 1.2 kcal/mol and 1.8 kcal/mol for HFP and TFE respectively.

re

Thus, the explosive nature of the reaction must be due to the presence of fluorine molecules.

[76]. T (K) 85 85 150,160,170

(HFP)3+F2

160-190

Material Crystal TFE Crystal HFP Crystal (HFP)2

ur na

Reactants TFE+F2 HFP+F2 (HFP)2+F2

lP

Table 3. Properties of fluorine reacting with pure components as a function of the temperature T

Explosion Explosion Oscillation in heat released + Increase heat release with increased F2 Rate and magnitude of heat release smaller than (HFP)2+F2

Jo

Supercooled liquid (HFP)3

Result

Calorimetric curves of fluorination of solid (HFP) 2 in the presence of different initial

concentrations of F2 show no heat release from fluorination at temperatures up to 110 K where the oligomer transitions into the supercooled liquid state [76]. Further increases in temperature give rise to a heat release region with an oscillating structure. The final stage begins at the temperature of (HFP)2 crystallization (124 K) and continues up to the melting point of crystalline (HFP) 2 at 17

176 K. The released heat is due to fluorination of (HFP) 2 as shown by comparison of the calorimetric curves for samples with different initial concentration of fluorine; increased fluorine concentration resulted in increased heat release. No reaction between F2 and glassy (HFP)3 occurs at 77 K. No appreciable heat release due to fluorination is observed at 150 K where (HFP) 3 transitions from a glassy solid to a supercooled liquid. Analysis of calorimetric curves of direct fluorination of (HPF) 2 and (HFP)3 shows that the

of

rate of heat release and quantity of heat release for (HFP) 3 are much smaller than that of (HFP)2.

ro

Heat release due to fluorination is observed in wide temperature intervals for solid solutions of TFE in (HFP)2 [76]. These temperature intervals occur at the same phase transitions

-p

temperatures as when TFE is not present. Calorimetric curves for TFE-(HFP)2 with F2 and TFE-

re

(HFP)2 show devitrification, crystallization, and melting of (HFP) 2 at 110 K, 124 K, and 176 K, respectively. The phase of both (HFP)2 and (HFP)3 does not change due to dissolution of TFE. The

lP

presence of TFE significantly increases the rate of heat release in the (HFP) 3 matrix, though fluorination of TFE in (HFP)3 is still three times slower than in (HFP)2.

ur na

2.3 Experimental: Fluorination of TFE in liquid perfluoroorganics Table 4 contains temperature ranges for different regimes of direct fluorination of TFE in HFP oligomers, perfluoroaromatic compounds (PFB, PFT), and perfluoroalkanes (PFH, PFO, C 9F20). Three different types of products are formed during TFE fluorination in various liquid perfluoroorganic

Jo

compounds [76] as shown in Table 4. TFE fluorination in oligomers of HFP forms primarily C2F6. The second contains approximately 50% C2F6 with the remaining TFE destroyed, and this happens when perfluoroaromatic compounds (PFB, PFT) are used as the solvent. Significant destruction of TFE to form CF4, the third group, occurs when linear (PFH, PFO) and branched (C 9F20) are used as the solvent. For all solvents, a portion of the TFE could combust with fluorine in the reactor

18

head space. As a result, soot, tar, and other solid products were observed on the interior surface of the reactor.

Table 4. Reaction characteristics of direct fluorination of TFE in various diluents as a function of the temperature T [76]. T (K) 203-278 283

Result <5% TFE destruction Increased TFE destruction, (HFP)x reacts. TFE destruction increased with F2 concentration

TFE+PFB/PFT+F2

<260

TFE+PFB/PFT+F2 TFE+PFH/PFO/C9F20+F2 TFE+PFH/PFO/C9F20+F2

260 <260 260

~50% C2F6 produced. Primary side product is CF4 Explosion ~80% CF4, 10% C2F6 Explosion

re

-p

ro

of

Reactants TFE+(HFP)x+F2 TFE+(HFP)x+F2

The destruction of TFE in HFP oligomer solvents below 278 K may be due to F2 gas phase

lP

combustion with TFE vapors above the liquid reaction mixture. Use of pure HFP oligomers or a mixture of HFP oligomers resulted in the same products. No phase transitions occur in the HFP

ur na

oligomer reaction mixture between 278 K and 283 K, therefore the change in reactivity is not due to this physical phenomenon. The change in reaction products at 283 K may be due to a change in the partial pressure of the reactants causing gas phase reactions to increase or an increase in reactive CF3 radical concentration. The increased concentration of CF3 is likely due to cleavage

Jo

of the HFP oligomer diluent. The amount of TFE destroyed by F2 combustion increases as F2 concentration increases, shifting from 2 mol% combusted TFE at a 50/50 mol% ratio of TFE/F2 to 12 mol% at a TFE/F2 ratio of 45/55 mol%. Increased TFE destruction with increased F2 concentration matches the equilibrium products from Gibbs free energy minimization curves in Figure 1. Increased pressure of F2 above the reaction mixture and increased temperature increased

19

fluorination rate exponentially and linearly respectively. (HFP) 3 destruction begins at lower temperatures when TFE is present due to reactions between fluorine and TFE promoting conditions for the combustion of (HFP)3. Other fluorinated solvents do not work as well as HFP oligomers [76]. Perfluoroaromatic compounds are able to trap active centers but the resulting radicals are still reactive, unlike the long-lived radicals (LLRs) that result from active sites trapped by HFP oligomers. No threshold is

of

present between soft and hard fluorination of TFE with variation in temperature or reactant

ro

concentration ratios. The rate of fluorine addition to the double bond of TFE is slower than the rate of TFE rupture in perfluoroalkane and perfluoroaromatic solvents leading to the formation of CF4.

-p

Though perfluoroalkanes and perfluoroaromatics could absorb the energy from excited products,

re

e.g. C2F6*, they are unable to effectively trap active centers and terminate the chain process EPR studies show that the LLRs noted above are formed during fluorination of HFP

lP

oligomers and TFE in HFP oligomers [53-,54,55,56,57,59-,60,61,74,76]. Formation of LLRs was also observed during organic synthesis where they were unable to dimerize [78,79,80]. The EPR

ur na

spectra of fluorinated or radiolyzed (HFP)2 shows the presence of doublet radicals [81] formed by addition of a fluorine atom to the double bond in (HFP) 2 (HFP)2 + F• → ((CF3) 2CF)C•F(C2F5) (LLR (1))

(80)

as well as the LLR(2) radical formed when (HFP) 3 “traps” a fluorine atom

Jo

(HFP)3 + F• → ((CF3)2CF)2)C•C2F5 ( LLR(2))

(81)

(HFP)3 is present at ~1% in the commercial (HFP)2 used in experiments. LLR(1) and LLR(2) form above the crystallization temperature of (HFP)2, 125 K, which also corresponds to the temperature where heat is released upon fluorination. The concentration of LLR(1) increases when (HFP)2 begins to melt and is a liquid, but both LLR(1) and LLR(2) concentration declines above 215 K

20

once heat release from the reaction stops. The concentration of LLR(2) is more than an order of magnitude less than the concentration of LLR(1) and remains constant as temperature varies. The EPR spectra [53] of direct fluorination of (HFP)3 shows the presence of LLR(2), which has high thermal and chemical stability []. Formation of LLR(2) during direct fluorination of TFE in (HFP)3 was studied in solid and liquid phase reactions [76]. The solid phase study was performed by slowly warming a mixture of

of

F2, TFE, and (HFP)3 from 77 K to 300 K. LLR(2) started to form at the glass transition temperature

ro

of vitrified pure (HFP)3 which was then followed by heat release due to fluorination. A rapid increase in LLR(2) concentration was observed above 220 K and an exponential increase in

-p

concentration of LLR(2) (up to 1.5x1019 radicals/g) was observed at 298 K for pure (HFP) 3

re

fluorination. The concentration of LLR(2) was equal to the concentration of LLR(2) in the analogous experiment without TFE. The liquid phase reaction was studied by bubbling gaseous

lP

TFE (50 mol%) and F2 (50 mol%) through liquid (HFP)3 in a reactor prior to transferring the sample to an EPR ampoule as supplying F2 gas directly to TFE/(HFP)3 in the EPR ampoule at 300

ur na

K resulted in an explosion. Most F2 was consumed by TFE as the LLR(2) concentration in the TFE containing reaction was four orders of magnitude smaller than LLR(2) concentration in the reaction without TFE.

The EPR spectra and calorimetry results confirm that a correlation exists between

Jo

formation of LLRs and heat release during fluorination in vitrified matrixes of HFP oligomers. LLRs play an important role in the safe direct fluorination of TFE. The double bonds in HFP oligomers moderate the fluorination of TFE through the formation of LLRs. It is important to note that while LLRs do not react with most radical species, known LLRs are somewhat reactive with molecular fluorine. LLR reactivity with molecular fluorine allows for reaction chain propagation,

21

but the low chemical reactivity will slow propagation. Diluents that do not contain double bonds, such as saturated analogs of HFP and other perfluoroalkanes, lead only to explosive fluorination of TFE. 2.4 Features of the low temperature fluorination of TFE in a vitrified matrix of HFP oligomers The reasons that molecules of HFP oligomers are an effective diluent for the safe direct fluorination of TFE are due to the presence of the double bonds in the HFP oligomers and the

of

resulting highly branched structures resulting from fluorination of these double bonds in the HFP

ro

oligomers. Comparison of data for fluorination of TFE in (HFP)3 and TFE in C9 F20 (the saturated analog of (HFP)3) helps elucidate the role of double bonds in highly branched diluents. Using

-p

C9F20 as diluent causes more sample burning than a diluent of (HFP) 3, 30 mol% compared to 26

re

mol%, and less C2F6 production, 8 mol% compared to 97 mol% for (HFP)3 [Error! Bookmark not defined.76]. These results confirm that a highly branched diluent structure alone does not

lP

provide an effective environment for the safe fluorination of TFE. Unsaturated bonds in the diluent alone, e.g. C6F5CF3, do not provide an effective environment for the safe fluorination of TFE. TFE

ur na

burning was approximately equal between diluents of C9F20 and C6F5 CF3, 30 and 37 mol%, respectively, and C2F6 yield increased dramatically from 8 mol% to 35 mol% [76]. Use of C6F5CF3 as diluent instead of (HFP)3 led to increased burning of the TFE and to a much lower yield of C2F6. On the basis of these results, both a branched structure and unsaturated bonds are necessary to

Jo

provide an effective environment for the safe fluorination of TFE. HFP and its oligomers contain double bonds surrounded by branched perfluorinated groups which provide such a suitable environment. The unsaturated bonds in HFP oligomers are active radical traps, forming LLRs, allowing for the safe direct fluorination of TFE. HFP oligomers release small amounts of heat upon fluorination and decrease the possibility of the reaction medium overheating. On the basis of the

22

energetic results in Table 1, addition of molecular fluorine to the double bond of TFE and (HFP)2 are 1.7 and 1.3 times as exothermic as addition of molecular fluorine to the double bond of (HFP) 3 respectively. The calculations also show that addition of a fluorine radical to the double bond of TFE and (HFP)2 are 1.4 and 1.1 times as exothermic as addition of a fluorine radical to (HFP) 3 respectively, limiting heat released by the reaction if (HFP) 3 is used. Fluorination of the solid mixture of TFE and (HFP)2 releases more heat and occurs more

of

rapidly than fluorination of pure (HFP) 2. Fluorination of pure (HFP)2 begins after reaching

ro

crystallization temperature whereas fluorination of the vitrified solution of TFE in (HFP) 2 begins at a lower temperature than the crystallization temperature of (HFP) 2. All samples containing TFE

-p

have higher total heat release and higher rate of heat release than samples that do not contain TFE.

re

This increase in total heat release and rate of heat release for samples containing TFE does not lead to explosion characteristics if fluorination is carried out in a vitrified matrix of oligomers of

lP

HFP, particularly the dimer, at 85 K.

Three peaks are observed in oscillations in the heat released during the melting process of

ur na

TFE in (HFP)2 in the presence of F2 are also observed during the melting process of pure (HFP)2 in the presence of F2. The three peaks shift toward lower temperatures during fluorination of samples containing TFE. The first peak begins at the temperature that (HFP) 2 crystallizes from the supercooled state. We suggest that the formation of the vibrational excited state intermediate C2F6*

Jo

from fluorination of TFE requires a lower activation energy than the formation of C 6F14* resulting from fluorination of (HFP)2. As a result, the falloff associated with this process ends much faster, whereas the initiation of the chain decays of the excited perfluoroalkane (C2F6*) begins earlier. Furthermore, the fluorination of (HFP) 2/TFE mixtures can be better controlled as heat can be removed from the reacting sites by the melting of (HFP) 2. We suggest that these are the reasons

23

for the shifting of the other peaks to the low temperature region. There is a marked similarity of the kinetic curves of fluorination of pure (HFP) 2 to its mixture with TFE due to the fact that fluorination of TFE takes place in parallel with the fluorination of (HFP)2 in the same matrix. Fluorination of pure, crystalline, TFE at 85 K may have resulted in an explosion as the high ordering found in the TFE crystals and increased mobility of fluorine molecules at their boiling point allow for C2F6* to form quickly. When highly excited C2F6* is formed quickly it can

of

decompose in a variety of ways leading to formation of many radical species that then react

ro

exothermically with TFE and other radicals causing an explosion. The absence of crystalline TFE in the (HFP)2/TFE mixture could be the reason that large amounts of C2F6* are not formed and an

-p

explosion does not occur even at high temperatures and high concentrations of fluorine. Limited

re

formation of C2F6* is in part due to dilution of the active TFE with inactive (HFP)2 and the termination of chain propagation due to the formation of LLR(1) upon the addition of a fluorine

lP

radical to the double bond of (HFP)2.

The low temperature transition of the glassy matrix of oligomers into a supercooled liquid

ur na

makes it possible for fluorine to dissolve in the liquid and react with dissolved TFE. Crystallization of the supercooled liquid can help stabilize the C2F6* and allow it to more readily react. C2F6* formation is only likely to occur on the surface of pure crystalline TFE due to the absence of an inert matrix to dissolve fluorine. The lack of an inert matrix to dissipate energy from fluorination

Jo

can lead to an explosion.

The primary role of HFP oligomers as an effective inert medium for the safe fluorination

of TFE is to prevent chain branching by trapping fluorine radicals formed in the reaction medium. Fluorine radicals trapped by HFP oligomers form LLR(1) and LLR(2) which terminate both the branching and reaction chain processes.

24

Spontaneous fluorination of TFE can be initiated in more ways in the liquid phase than in the low temperature solid phase. Chain fluorination of liquid phase and solid phase TFE occur by the same reactions (Table 1), though which reaction dominates depends upon the fluorination conditions. Non-HFP oligomer diluents are not capable of creating a safe, effective, environment for the direct fluorination of TFE. Analysis of experimental data, computational data, and literature

of

data [20,53-,54,55,56,57,61,76,87] suggests that the optimal diluent for safe direct liquid phase

ro

fluorination of TFE is (HFP)3. (HFP)3 is able to effectively trap F and CF3 radicals to terminate the chain branching process.

-p

2.5 Mechanism of solid phase low temperature fluorination of crystalline TFE Fluorination

re

begins at 85 K on the surface of crystals of TFE or HFP in an excess of liquid fluorine and finishes with an explosion. A sharp heat release is observed near 85 K due to fluorination of crystals of

lP

TFE or HFP. This suggests a branched chain mechanism for the spontaneous fluorination process. Fluorination of crystalline TFE generates highly reactive F and other radicals during chain

ur na

reactions resulting in strongly exothermic fluorination. The calculated reaction energies (Table 1) show that the reaction of F2 with TFE is exothermic for reactions (11) to (14). Reaction (11) is the energy to form the highly activated intermediate C2F6 *. Reactions (12) through (14) form the reactive species :CF2, CF3, C2F5, and

Jo

F from the decomposition of C2F6 * with fluorine that results in chain propagation. The sharp increase in the rate of heat release resulting in an explosion can be the result of chain branching processes, reactions (15) and (17), which then provide more reactive species to participate in exothermic reactions (15) to (27). Chain termination reactions are (28) to (38) and (40).

25

CF4 is the primary product of fluorination of pure TFE. CF4 is a product of chain initiation reaction (12), chain propagation reaction (19), and chain termination reaction (32). Reactions involving difluorocarbene are important for production of CF4. Difluorocarbene is not present at equilibrium at low (<1000 K) temperatures for any ratio of C:F, Figure 1, but difluorocarbene is likely present prior to reaching equilibrium or in areas with high local temperatures. CF4 producing

of

reactions, (19) and (32), both involve CF3 that can be produced by reactions (15) and (18) that have difluorocarbene as a reactant. The desired product, C2F6, is produced by chain propagation

ro

reaction (20) and chain termination reactions (28) and (34). Longer chain carbon products (C3 and C4) are produced from TFE reaction products by reactions (21) through (27), (29), (30), and (35).

-p

The chain branching mechanism has not previously been used to explain solid phase, low

re

temperature TFE fluorination as it was considered to be just a burning process. The mechanism of energetic chain branching is characteristic of the fluorination of olefins in the absence of inert

lP

solvents in the gas and liquid phases. For example, highly energetic chain branching can happen in the gas phase reaction of F2 with C2Cl4 or C2H2Br2 [88] only in the presence of excess F and Cl

ur na

or F and Br, respectively.

The possibility of formation of complexes of F2 with various species including TFE and the matrix fluorocarbon exists at the low temperatures used in these experiments. The potential role of molecular complexes in the fluorination process was examined by predicting the binding

Jo

energy of TFE with F2. The geometry of the complex between F2 and TFE was optimized at the MP2/aug-cc-pVnZ (n=D, T) levels [] starting at distances of 2 Å and 4 Å between the F2 and TFE. In both cases, the geometry optimized to a complex with an interaction distance of about 3 Å, as expected from typical van der Waals radii. The value of the complexation enthalpy is -1.1 kcal/mol and the value of the complexation free energy is 0.4 kcal/mol at 77 K at the MP2/aug-cc-pVTZ

26

level. Although the calculations are for the free gas phase dimer, the results show that the complexation free energy is positive even at 77 K so it is unlikely that F2/TFE complexes play a major role in the reactions. The above discussion for direct fluorination is in contrast to the mechanism for direct chlorination where the role of such complexes has been demonstrated experimentally [92]. The available data for direct chlorination shows three basic mechanisms: radical, ion and molecular.

of

The relative contribution of a particular mechanism depends on the temperature, the concentrations

ro

of reactants, the nature and polarity of the reaction medium, the phases of the system, and the nature of the olefin. The C-Cl bond energies are comparable to C-H bond energies so chlorine and

-p

newly generated organic free radicals are available to initiate the chain chlorination of olefins

re

[93,94]. The role of molecular complexes in the formation of the free radicals during direct chlorination has been considered [95]. The ionic mechanism is conventional for chlorination in

lP

polar media [95], with the rate-limiting step being the formation of the ion pair. The degree of charge separation in the transition state is close to unity. The molecular mechanism of chlorination

ur na

involves the formation of the products directly from a molecular complex, bypassing dissociation into ions or radicals. Such a process is only possible when the energy for breaking the reactant bonds in the transition state is compensated by the energy of the forming product bonds. It has been experimentally confirmed [96] that the low-temperature chlorination of perfluoroolefins

Jo

requires an initiation step and does not happen spontaneously, in contrast to the spontaneous fluorination of perfluoroolefins at low temperatures [59-,60,61]. The existence of molecular complexes between olefins and halogens in solution and in the solid phase has been shown experimentally for chlorination [92] and bromination [97] but not for fluorination. As fluorination differs from chlorination in part due to different bond dissociation energies of F2 and Cl2 and

27

differences in the C-F and C-Cl bond energies, the use of chlorination mechanisms to explain fluorination requires additional experimental verification. 2.6 Mechanism of the solid phase low temperature fluorination of crystalline HFP A radical chain or chain branching mechanism cannot be applied to the direct fluorination of crystalline HFP because it is unable to participate in its own radical chain polymerization [98], unlike TFE [99]. In this case, the highly branched and inactive dimer or trimer LLRs of HFP could be formed in the

of

first steps of the chain propagation of HFP polymerization and they terminate the propagation as

ro

follows: HFP + (γ) → RF + products

chain initiation

(82b)

chain termination

(82c)

-p

HFP + RF → RF F2C-CF(CF3)

re

HFP + RFC F2-CF(CF3) → RFCF2CF(CF3)-C(CF3)2

(82a)

The product of reaction (82c) is LLR(2). This explains the inertness of HFP to reactions with

lP

branched fluorine containing radicals which are formed as a result of its oligomerization. Termination of the chain process in reaction (11) cannot be realized during the reaction of fluorine

ur na

with the perfluoropropyl radicals formed on addition of fluorine to HFP. Reactions (36-79) in Table 1 contain HFP oligomer radical formation reactions and reactions involving HFP oligomer radicals. Both isomers of (HFP)2, A(HFP)2 and B(HFP)2, and the three isomers of (HFP)3, A(HFP)3, B

(HFP)3, and C(HFP)3, were considered for Table 1. The stability of C(HFP)3 radicals are likely

Jo

low as they were not found experimentally and are not as branched as A(HFP)3 and B(HFP)3 radicals. Reactions (37, 38, 48, and 49) and reactions (55, 56, 68, 69, 74, and 75) demonstrate that the addition of F to (HFP)2 and (HFP)3, respectively, to form radical species are exothermic. Loss of CF3 from the radicals produced by addition of elemental fluorine to (HFP) 2 and (HFP)3, reactions (39 and 50) and (57, 58, 70, and 76-79) for (HFP)2 and (HFP)3 respectively, is 28

endothermic. These reactions are unlikely to participate in the chain propagation mechanism that is responsible for overheating and explosions in the direct fluorination of TFE. The composition of products formed in the initial steps of fluorine addition to the double bond of the olefins cannot be determined as only the explosive regime products can be detected. As a result, the nature of the explosive process cannot be established unambiguously from experiment. Calorimetric studies of the melting of crystalline perfluoroolefines in the presence of

of

fluorine show that the fluorine starts to react violently with olefins only near its boiling point of

ro

85 K, although the possibility of initiation of fluorination at temperatures lower than 85 K has not been eliminated. The temperature difference between 85 K and 77 K is small, which makes it

-p

difficult to detect exactly when fluorination begins. As a result, a rise in energy due to reaction

re

could occur faster than can be detected by the thermocouple in use. 3. Conclusions

lP

Mechanisms for direct fluorination of TFE in vitrified matrixes and moderate temperature liquid phases are developed based on the concepts of formation of active intermediates, radical

ur na

chains, and exothermic elementary steps. Gibbs free energy minimization indicates that the gas phase equilibrium products of a low C:F ratio mixture of C2F4 and F2 contains CF4, C2F6, and C3F8 at low temperature and F and :CF2 at high temperature. The gas phase equilibrium products of a high C:F ratio mixture of C2F4 and F2 contains CF4 and F2 at low temperature and F and :CF2 at

Jo

high temperature. Gibbs free energy minimization combined with the experimental results provides estimates of the effective local temperatures for direct fluorination reactions. On the basis of a 2C:6F atomic ratio, Figure 1a, the effective local temperatures for HFP oligomers, perfluoroaromatic solvents, and straight chain perfluoroalkane solvents are 800 K, 1000 K, and 1500 K respectively. CF3 radicals do not appear at low temperature in the Gibbs free energy

29

minimization, Figure 1, but are likely present prior to equilibrium to produce C3 and higher products. A branched chain mechanism is suggested for the spontaneous fluorination process. Highly active species are produced upon the decomposition of the highly activated intermediate C2F6*. These highly active species result in exothermic chain propagation reactions and can lead to exothermic chain branching reactions resulting in explosions. Chain termination reactions are

of

proposed with products ranging from F2 to short chain fluorocarbons or long-lived radicals based

ro

upon the HFP oligomer solvent. Difluorocarbene is important in the formation of CF 4 from direct fluorination of pure TFE. The results confirm the use of HFP oligomers as a diluent for direct

-p

fluorination of TFE as they act as radical traps and can remove some of the excess heat produced

re

by the branched chain fluorination of TFE. In the cases studied, the reaction mechanism is considerably simplified and achieves the high processability and safety desired for direct

lP

fluorination. Competition between reactions is the main reason for differences in mechanism depending upon reaction conditions. Overheating of the reaction mixture is the first step in

ur na

uncontrolled fluorination. The likelihood of overheating is reduced by including relatively inert diluents of HFP oligomers which can trap radicals and slowing down or eliminating chain branching.

4. Computational Methods

Jo

The electronic structure calculations were initially done at the density functional theory

levels with the B3LYP [71,72] functional and the DZVP2 basis set [73]. The molecular geometries were initially optimized at the DFT level. These geometries were used as input for the composite, correlated G3(MP2) [67] and G4 [68] molecular orbital theory level calculations. All reaction energy calculations were done with the Gaussian09 program system [100]. Computational boiling

30

points were determined using COMSO-RS [101] as implemented in ADF2016 []. Geometries used for boiling point calculations were optimized with B3LYP/DZVP2 in Gaussian09. Gibbs free energy minimization was performed using equations (83) and (84). ΔGi = ΔHi + T(ΔSi)

(83)

j ΔG = ∑i=1 ni (ΔGi + R ∗ T ∗ ln (

j

ni

∑i=1 ni

))

(84)

of

ΔG represents Gibbs free energy, ΔH is enthalpy, T is absolute temperature, ΔS is entropy, n is number of moles, R is the gas constant, j is the number of species, and subscript i represents the

ro

species. Equation (83) was evaluated for each component at each temperature and was then

-p

substituted into equation (84) to calculate the Gibbs free energy of the mixture [105]. The Gibbs free energy of the mixture was minimized by varying the amount of each component, subject to a

re

mole balance, using the function fmincon in MATLAB R2019a with the interior-point

lP

minimization algorithm []. Enthalpy correction terms and entropy with respect to temperature for each component are provided in the supporting information, Tables S5 and S6.

ur na

Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Jo

Acknowledgement

The authors thank the Cooperative Grants Program of the U.S. Civilian Research and Development Foundation for financial support. (Grant No RUC1-7093-MO-13). D. A. Dixon thanks the Robert Ramsay fund of The University of Alabama for partial support. The computational work at UA was supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, U.S. Department of Energy (DOE) under the DOE BES Catalysis Center 31

Program by a subcontract from Pacific Northwest National Laboratory (KC0301050-47319). Supporting Information The best available heats of formation for C2F6, CF4, CF3-CF2, F, F2, C2F4, :CF2, CF3, СF3СF2СF2, СF3СFСF3, C3F8, CF3CF2CF2CF2, CF3CF=CF2, C4F10, and C3F6 cyclic are given in the supporting information. B3LYP/DZVP2 optimized geometries and enthalpies for all compounds, heats of formation and calculated entropies for compounds used in

of

the Gibbs Free Energy minimization, comparison of temperature independent and dependent enthalpy and entropy used in the Gibbs Free Energy minimization, and total moles of gas present

ro

at equilibrium as a function of temperature for the Gibbs Free Energy minimization are presented

re

G3(MP2) are provided in the Supporting Information.

-p

in the supporting information. Sample Gaussian input files for C2F4 for B3LYP/DZVP2 and

lP

References

[1] R. Chambers, Fluorine in organic chemistry, Wiley-Blackwell, Oxford, 2004.

ur na

[2] G. A. Olah, R. D. Chambers, G. K. S. Prakash, Synthetic Fluorine Chemistry, WileyInterscience, New York, 1992.

[3] P. Kirsch, Modern Fluoroorganic Chemistry: Synthesis, Reactivity, Applications, WileyVCH, Weinheim, FRG, 2004.

Jo

[4] T. Nakajima (Ed.), Fluorine-Carbon and Fluoride-Carbon Materials: Chemistry, Physics, and Applications, Marvel, Dekker, New York, 1994. [5] R. D. Chambers, Organofluorine Chemistry: Techniques and Synthesis, Topics in Current Chemistry, Vol. 193, Springer, Berlin, 2013.

32

[6] M. Hudlický, A. E. Pavlath, Chemistry of Organic Fluorine Compounds II, ACS Monograph 187, American chemical Society, Washington, D.C., 1995. [7] R. D. Chambers, M. A. Fox, G. Sandford, J. Trmcic, A. Goeta, J. Fluor. Chem., 128 (2007) 29-33. [8] G. Sandford, J. Fluor. Chem., 128 (2007) 90-104.

[10] Q. Shao, Y. Huang, Chem. Commun. 51 (2015) 6584-6586.

of

[9] W. R. Dolbier Jr., J. Fluor. Chem., 126 (2005) 157-163.

ro

[11] T. Liang, C. N. Neumann, T. Ritter, Angew. Chem. 52 (2013) 8214-8264.

[12] I. Ojima, J. R. McCarthy, J. T. Welch, Biomedical Frontiers of Fluorine Chemistry, ACS

-p

Symposium Ser. 639, American Chemical Society, Washington, D.C. 1996.

re

[13] M. Hudlický, Fluorine Chemistry for Organic Chemists, Oxford University Press, Oxford, 2000.

lP

[14] V. A. Soloshonok, K. Mikami, T. Yamazaki, J. T. Welch, J. Honek, Current Fluoroorganic Chemistry: New Synthetic Directions, Technologies, Materials, and Biological Applications,

ur na

ACS Symposium Ser. 949, American Chemical Society, 2007. [15] J. T. Welch, S. Eswarakrishnan, Fluorine in Bioorganic Chemistry, Wiley-Interscience, New York, 1991.

[16] R. E. Banks, B. E. Smart, J. C. Tatlow (Eds.), Organofluorine Chemistry: Principles and

Jo

Commercial Applications, Plenum Press, New York, 1994. [17] F. M. Mukhametshin, Russ. Chem. Rev., 49 (1980) 668-682. [18] A. Tressaud, E. Durand, C. Labrugère, A. P. Kharitonov, G. V. Simbirtseva, L. N. Kharitonova, M. Dubois, Acta Chim. Slov., 60 (2013) 495-504. [19] S. Rozen, Асc. Chem. Res., 21 (1988) 307-312.

33

[20] S. P. von Halasz, F. Kluge, T. Martini, Chem. Ber., 106 (1973) 2950-2959. [21] G. G. Hougham, P. E. Cassidy, K. Johns, T. Davidson (Eds.), Fluoropolymers 1: Synthesis, Kluwer Academic, New York, 1999. [22] J. Maity, C. Jacob, C. K. Das, R. P. Singh, J. Appl. Polym. Aci., 107 (2008) 3739-3749. [23] D. G. Castner, D. W. Grainger, Fluorinated surfaces, coatings, and films ACS Symposium Ser. 787, American Chemical Society, Washington, DC, 2001.

of

[24] H. Kawa, U.S. Patent 5,455,373, 1995.

ro

[25] T. Okazoe, Proc. Jpn. Acad., Ser. B, 85 (2009) 276-289. [26] T. Okazoe, J. Fluor. Chem. 174 (2015) 120-131.

-p

[27] R. E. Banks, S. N. Mohialdinkhaffaf, G. S. Lal, I. Sharif, R. G. Syvret, J. Chem. Soc.,

re

Chem. Commun. (1992) 595-596.

[28] W. J. Middleton, J. Org. Chem., 40 (1975) 574-578.

lP

[29] W. J. Middleton, E. M. Bingham, Org. Synth., 50 (1988) 440-441. [30] M.G. Costello, G.G.I. Moore, U.S. Patent 5,399,718, 1995.

ur na

[31] R. E. Banks, J. C. Tatlow in Organofluorine Chemistry: Principles and Commercial Applications, R. E. Banks, B. E. Smart, J. C. Tatlow (Eds.), Plenum Press, New York, 1994. p.25-55.

[32] V. A. Volodina, A. A. Kozlovsky, S. I. Kuzina, A. I. Mikhailov, Chimiya visokich energii.

Jo

42 (2008) 353-360 (in Russian).

[33] X. Wang, Y. Chen, Y. Dai, Q. Wang, J. Gao, J. Huang, J. Yang, X. Liu, J. Phys. Chem. C, 117 (2013) 12078-12085. [34] N. Ishikawa, Fluorine compounds. Synthesis and Application, Translated from Japan, Mir, Moscow, 1990, p.407(in Russian).

34

[35] A. I. Rakhimov, Chemistry and technology of fluorine containing organic compounds, Chimiya, Moscow, 1986, p. 272(in Russian). [36] U. Lennard, K. Charts, Organic chemistry of fluorine, Mir, Moscow,1972, p. 480 (in Russian). [37] A. N. Ilyin, A. D. Kuznetsov, V. F. Denisenkov, S. M. Nurgaliyeva, G. I. Kaurova, D. D. Moldovskii, T. A. Bispen, RF Patent. 2,280,030, 2006.

of

[38] M. Anand, J. P., I. J. Brass in Organofluorine Chemistry: Principles and Commercial

p.469-481.

-p

[39] J. P. Hobbs, M. Anand, Eng. Plastics. 5 (1992) 247-258.

ro

Applications, R. E. Banks, B. E. Smart, J. C. Tatlow (Eds.),Plenum Press, New York, 1994

re

[40] A. P. Kharitonov. J. Fluor. Chem. 103 (2000) 123-127.

[41] A. P. Kharitonov, Yu. L. Moskvin, G. A. Kolpakov, RF Patent. 1,754,191, 1990.

Raton, FL, 2010.

lP

[42] Y. R. Luo, Comprehensive Handbook of Chemical Bond Energies; Taylor & Francis: Boca

ur na

[43] R. J. Lagow, J. L. Margrave, Prog, Inorganic Chem., 26 (1979) 161-210. [44] D. D. Moldavskii, G. T. Kaurova, T. A. Bispen, G. G. Furin, J. Fluor. Chem. 63 (1993) 193201.

[45] T. A. Bispen, D. D. Moldavskii, G. G. Furin, J. prikladnoi chimii 71 (1998) 1334-1342 (in

Jo

Russian).

[46] V. Zakharov, A. K. Denisenkov, P. M. Novikov, Russ. J. Org. Chemistry, 30 (1994) 18441847.

[47] A.E. Shilov, Modern problems of Physical Chemistry, Chimiya, Moscow, 1985 (in Russian) [48] T. R. Bierschenk, T. J. Juhlke, H. Kawa, R. J. Lagow, U.S. Patent 5,053,536, 1991.

35

[49] M. G. Costello, G. G. I. Moore, U.S. Patent 5,362,919, 1994. [50] T. R. Bierschenk, T. Juhlke, H. Kawa, R. J. Lagow, U.S. Patent 5,322,903, 1994. [51] A. C. Sievert, W. R. Tong, M. J. Nappa, J. Fluor. Chem., 53 (1991) 397-417. [52] T. Ono, Chim. Oggi, 21 (2003) 7-8, 39-43. [53] K. V. Scherer, Jr., T. Ono, K. Yamanouchi, R. E. Fernandez, P. Henderson, H. Goldwhite, J. Amer. Chem. Soc. 107 (1985) 718-719.

of

[54] K. V. Scherer, Jr., J. Fluor. Chem., 33 (1986) 298-301.

ro

[55] K. V. Scherer, Jr., R. Fernandez, P.B. Henderson, P.I. Krusic, J. Fluor. Chem., 35 (1987) 7. [56] S. R. Allayarov, I. V. Sumina, I. M. Barkalov, Yu. L. Bakhmutov, M. K. Asamov, Izv.

-p

Vyssh. Uchebn. Zaved., Khim, Khim. Tekhnol. 32 (1989) 26 (in Russian), Chem. Abstr. 112

re

(1990) 197451.

[57] V. F. Zabolotskikh, A. S. Kochanov, A. V. Tiunov, I. V. Markin, ZH ORG KH, 30 (8),

lP

(1994) 1219-1220 (in Russian).

[58] N. Ishikawa, M. Maruta, J. Syn. Org. Chem. Jpn., 39 (1981) 51-62 (in Japanese).

ur na

[59] S. R. Allayarov, I. M. Barkalov, I. P. Kim. Mendeleev Comm. 2 (1992) 139-141. [60] S. R. Allayarov, Russ. J. Org. Chem. 30 (1994) 1147-1155. [61] S. R. Allayarov, I. M. Barkalov, I. P. Kim, J. Fluor. Chem. 96 (1999) 57-60. [62] S. R. Allayarov, T. A. Konovalova, A. Waterfield, A.L. Focsan, L. D. Kispert, D.A. Dixon,

Jo

J.S. Thrasher, J. Fluor. Chem. 127 (2006) 1294-1301. [63] S. I. Kuzina, A. I. Mikhailov, V. I. Goldanskii, Dokl. An. SSSR. 321 (1991) 1022-1024 (in Russian).

[64] G. B. Sergeev, V. V. Smirnov, Molecular halogenation of olefins, Moscow State University, Moscow, 1985, p.240 (in Russian).

36

[65] S. I. Kuzina, A. P. Kharitonov, U. L. Moskvin, A. I. Mikhailov, Izvestiya RAN. Seriya Chimicheskaya. (1996) 1714-1718 (in Russian). [66] S. P. Sander, R. R. Friedl, J. P. D. Abbatt, J. R. Barker, J. B. Burkholder, D. M. Golden, C. E. Kolb, M. J. Kurylo, G. K. Moortgat, P. H. Wine, R. E. Huie, V. L. Orkin, Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies: Evaluation Number 17; JPL

California Institute of Technology: Pasadena, CA June 10, 2011.

of

Publication 10-6, National Aeronautics and Space Administration, Jet Propulsion Laboratory,

ro

[67] L. A. Curtiss, P. C. Redfern, K. Raghavachari, V. Rassolov, J. A. Pople, J. Chem. Phys. 110 (1999) 4703-4709.

-p

[68] L. A. Curtiss, P. C. Redfern, K. Raghavachari, J. Chem. Phys. 126 (2007) 084018-084030.

re

[69] D. Feller, K. A. Peterson, and D. A. Dixon, J. Phys. Chem. A, 115 (2011) 1440-1451. (Correction, 3182).

lP

[70] D. Feller, K. A. Peterson, and D. A. Dixon, J. Chem. Phys., 129 (2008) 204105-204137. [71] A. D. Becke, J. Chem. Phys. 98 (1993) 5648-5652.

ur na

[72] C. Lee, W. Yang, R. G. Parr, Phys. Rev. B. 37 (1988) 785-789. [73] N. Godbout, D. R. Salahub, J. Andzelm, E. Wimmer, Can. J. Chem. 70 (1992) 560-571. [74] S. R. Allayarov, D. A. Gordon, P. B. Henderson, R. E. Fernandez, V. E. Jackson, and D. A. Dixon J. Fluorine Chem., 180 (2015) 240-247.

Jo

[75] C. C. R. S. Rossi, L. Cardozo-Filho, R. Guirardello, Fluid Ph. Equilibria 278 (2009) 117128.

[76] S. R. Allayarov, I. P. Kim, I. V. Markin, A. A. Karnaukh, I. M. Barkalov, D. A. Dixon. Fluorine Notes. 72(5) (2010) 1-16. See http://notes.fluorine1.ru/contents/history/2010/5_2010/letters/index.html.

37

[77] PCR Inc., Research Chemicals Catalog 1990-1991, PCR Inc., Gainesville, FL, 1990, 1. [78] E. A. Avetisyan, B. L. Tumanskii, V. F. Cherstkov, S. R. Sterlin, L. S. German, Russ. Chem. Bull. 44 (1995) 558-559. [79] B. L. Tumanskii, N. N. Bubnov, V. R. Polishchuk, S. P. Solodovnikov, Russ. Chem. Bull. 30 (1981) 1821-1826. [80] G.G. Furin, Fluorine Notes, 14(1) (2001), 16 pages.

of

http://notes.fluorine1.ru/public/pdfs/14_1_en.pdf

ro

[81] S. R. Allayarov, I. M. Barkalov, Russ. Chem. Bull. 37 (1988) 1109-1114.

[82] S. R. Allayarov. Dissertation of degree Doctor of Chemical Sciences. Institute of chemical

-p

physics of Academy of Sciences of USSR, Moscow, (1993) 393 (in Russian).

re

[83] T. Ono, K. Ohta, J. Flour. Chem., 167 (2014) 198-202.

[84] T. Ono, H. Fukaya, M. Nishida, N. Terasawa, T. Abe, Chem. Commun., 13 (1996) 1579-

lP

1580.

[85] H. Mei, J. Han, S. White, G. Butler, V. Soloshonok, J. Fluor. Chem., 227 (2019) 109370-

ur na

109385.

[86] M. Okazaki, T. Ono, K. Komaguchi, N. Ohta, H. Fukaya, K. Toriyama, Appl. Magn. Reson., 36 (2009) 89-95.

[87] S. R. Allayarov, D. A. Gordon, T. E. Chernysheva, I. M. Barkalov, High Energy Chemistry,

Jo

37 (2003) 227-230.

[88] L. Ju. Rusin, A. E. Shilov, Doklady Akademii Nauk USSR. 172 (1967) 1340-1341 (in Russian).

[89] C. Møller, M. S. Plesset, Phys. Rev., 46 (1934) 618-622. [90] J. A. Pople, J. S. Binkley, R. Seeger, Int. J. Quantum Chem. (Supple. 10) 1976, 1-19.

38

[91] R. A. Kendall, T. H. Dunning, R. J. Harrison, J. Chem. Phys. 96 (1992) 6796-6806. [92] G. B. Sergeev, Y. A. Serguchev, V. V. Smirnov, Uspehi Chimii. 42 (1973) 1545-1573 (in Russian). [93] T. D. Stewart, M. K. Hanton, J. Amer. Chem. Soc. 53 (1931) 1121-1132. [94] A. N. Akopyan, A. N. Saakyan, A. A. Safaryan, J. obshei chimii. 32 (1962) 1098-1104 (in Russian).

of

[95] G. B. Sergeev, A. H. Hairy, V. V. Smirnov, I. N. Chizhova, F. Z. Badaev, Kinet. Catal. 23

ro

(1982) 547-555 (in Russian).

[96] S. R. Allayarov, I. P. Kim, I. M. Barkalov, L. M. Ivanova, A. N. Ilyin, Chimiya visokich

-p

energii. 27 (1993) 22-24 (in Russian).

re

[97] Ya. M. Kimelfeld, A. B. Mostovoi, Dokl. An. SSSR 213 (1973) 382- 385(in Russian). [98] S. R. Allayarov, I. M. Barkalov, S. I. Kuzina, N. N. Loginiva, A. I. Mikhailov, Khimiya

lP

Vysokikh energii. 22 (1988) 333-337 (in Russian).

[99] S. R. Allayarov, A. I. Bolshakov, I. M. Barkalov. Polymer science USSR. 29 (1987) 406-

ur na

412.

[100] Gaussian 09, Revision D.01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M.

Jo

Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J.

39

Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, D. J. Fox, Gaussian, Inc., Wallingford CT, 2009. [101] Klamt, A. Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design; Elsevier: Amsterdam, The Netherlands, 2005.

J.G. Snijders, T. Ziegler, J. Comput. Chem. 22 (2001), 931-967.

of

[102] G.te Velde, F.M. Bickelhaupt, E.J. Baerends, C. Fonseca Guerra, S.J.A. van Gisbergen,

ro

[103] C.Fonseca Guerra, J.G. Snijders, G. te Velde, E.J. Baerends, Theor. Chem. Acc. 99 (1998), 391-403.

-p

[104] E.J. Baerends, T. Ziegler, A.J. Atkins, J. Autschbach, D. Bashford, A. Bérces, F.M.

re

Bickelhaupt, C. Bo, P.M. Boerrigter, L. Cavallo, D.P. Chong, D.V. Chulhai, L. Deng, R.M. Dickson, J.M. Dieterich, D.E. Ellis, M. van Faassen, L. Fan, T.H. Fischer, C. Fonseca Guerra, M.

lP

Franchini, A. Ghysels, A. Giammona, S.J.A. van Gisbergen, A.W. Götz, J.A. Groeneveld, O.V. Gritsenko, M. Grüning, S. Gusarov, F.E. Harris, P. van den Hoek, C.R. Jacob, H. Jacobsen, L.

ur na

Jensen, J.W. Kaminski, G. van Kessel, F. Kootstra, A. Kovalenko, M.V. Krykunov, E. van Lenthe, D.A. McCormack, A. Michalak, M. Mitoraj, S.M. Morton, J. Neugebauer, V.P. Nicu, L. Noodleman, V.P. Osinga, S. Patchkovskii, M. Pavanello, C.A. Peeples, P.H.T. Philipsen, D. Post, C.C. Pye, W. Ravenek, J.I. Rodríguez, P. Ros, R. Rüger, P.R.T. Schipper, H. van Schoot,

Jo

G. Schreckenbach, J.S. Seldenthuis, M. Seth, J.G. Snijders, M. Solà, M. Swart, D. Swerhone, G. te Velde, P. Vernooijs, L. Versluis, L. Visscher, O. Visser, F. Wang, T.A. Wesolowski, E.M. van Wezenbeek, G. Wiesenekker, S.K. Wolff, T.K. Woo, A.L. Yakovlev, SCM, ADF2016; Vrije Universiteit: Amsterdam, The Netherlands, 2016; http://www.scm.com.

40

[105] McQuarrie, D. A.; Simon, J. D. Molecular Thermodynamics, 1st ed.; University Science Books, 1999. [106] MATLAB, version 2019A; MathWorks: Natick, MA, 2019. [107] MATLAB Optimization Toolbox, version 2019A; MathWorks: Natick, MA, 2019.

Jo

ur na

lP

re

-p

ro

of

[108] Matlab in Chemical Engineering at CMU. Finding equilibrium composition by direct minimization of Gibbs free energy on mole numbers. http://matlab.cheme.cmu.edu/2011/12/25/finding-equilibrium-composition-by-directminimization-of-gibbs-free-energy-on-mole-numbers/#3 (accessed July 25, 2019).

41