Received: July, 2011

Fluorine Notes, 2011, 78, 7-8

Forecasting Glass Transition Temperatures of Fluorocontaining Polymers

A. N. Kollar, V. A. Gubanov

Federal State Unitary Enterprise S.Y. Lebedev Research Institute for synthetic rubber (FSUE "NIISK")
e-mail: vniisk@vniisk.cplus.ru

Abstract: The analysis of T_c (T_g, Glass Transition Temperature) dependence on both length and structure of the chain connecting triazine rings in perfluorinated polymers synthesized by the authors made it possible to improve the algorithm for Tc calculation developed earlier by A.A.Askadskii and G.L.Slonimsky. The proposed variant of Tc calculation allows reliable forecasting of cold resistance behaviour of both carbochain- and heterochain-fluoropolymers and tailoring of promising materials with the best properties.

Keywords:fluoropolymers, structure - glass transition temperature, calculation of glass transition temperature, tailoring of advanced structures.

The synthesis of polymers with pre-designed structures is among of the modern chemistry and physics challenges. The Glass Transition Temperature (T_c) is one of the most significant polymer properties. T_cforecasting prior to the polymer synthesis, and reasoning from the chemical structure of its repeating units seems to be a topical problem. A considerable number of studies have already been devoted to the problems of T_c relation to the polymer chemical structure. In general, those calculations based on the assumption that the macromolecule repeating unit may be divided into a number of atomic groups with additive contributions to T_cindependent of the environment. Its mathematical expression is as follows:

Here T_ci is characteristic contribution of a group into T_c; and S_i is the mass coefficient assigned to the group.

In the most of polymers T_cis estimable with accuracy +20 K. The methods for the T_c calculation based on such assumption was considered in [1-5] along with some other methods. However, the main disadvantages of the techniques offered by those authors are their non-flexibility and low accuracy. Another method different from those mentioned was introduced by A.A.Askadskii and G.L.Slonimsky for the calculation of T_cin amorphous polymers [6]. Basing on the temperature dependence of polymer packing factor they derived an equation that relates the polymer T_cto some parameters of the chemical structure of a macromolecule repeating unit:

Here is the characteristic mole volume of the repeating unit made up of the volumes of atoms that enter into the composition of the repeating unit (Van der Waals volume);

- is an additive value (with volume dimensionality) related to the packing factor and to the coefficient of volumetric expansion of the polymer body (efficient volume of the chain repeating unit);

N_А is Avogadro constant equal to 6.023·10 ²³;
A is a parameter of any linear polymer equal to 1.435.

The computation is based on the assumptions suggested in [7]. Here is a sum of values K_xⁱ that characterize each element and every type of intermolecular interactions. The solution of a redundant equation system based on (1) resulted in K_xⁱ values shown in table 1.

Table 1. Numerical values for K_xⁱ [6].

#	Element or type of intermolecular interaction	Conventional sign	Numerical value (cm3/mole)
1 2 3 4 5 6 7 8	Carbon Oxygen (>C=O) Hydrogen Nitrogen Chlorine Hydrogen bond Dipole-dipole interaction* Coefficient of symmetry**	KXC KXO KXH KXN KXCl KXh KXd KXn	10.739 3.925 –1.248 9.520 7.242 7.338 7.827 10.500

* – K^Xd introduced in vinyl polymers when hydrogen in its main or side-chain is substituted with a radical of any type except phenyl.
** – K^Xn introduced in case that all aromatic cores in the main-chain are substituted in n-position.

In further studies [8, 9] two more increments were added: main-chain oxygen K^X_OO equal to minus 5.244, and main-chain nitrogen K^X_NO that is 2.185.

In [10] the computation scheme was further improved to determine T_cin fluoropolymers (mainly, perfluorinated triazine polymers, PFT). To this end some novel K_xⁱ were introduced, their numerical values were determined (Table 2) and T_c were calculated in a number of polymers.

Table 2. Numerical values for K_xⁱ [10]

#	Element or type of intermolecular interaction	Symbol	Numerical value (cm3/mole)
1 2 3 4 5	Fluorine Oxygen (in chain) Dipole-dipole interaction due to ≡CF group Dipole-dipole interaction due to –CF2– group ДDipole-dipole interaction due to –CF3 group	KXF KXO KXd1 KXd2 KXd3	2.944 0.215 2.080 3.312 3.610

For homotypic PTF polymers with hexafluoroethylene oxide (HFPO) in their main or side chains the calculated T_c deviated from its experimental value less than by 2%.However, PFT polymers with tetrafluoroethylene oxide (TFEO) links in their main chains and most of synthesized PFT do not fit in the above calculation scheme.

In table 3 experimental T_c values for some polymers synthesized by us are compared to T_c calculated using the published data [10].

Table 3. Experimental and calculated T_c in polymers.

From table 3 one may conclude that the available calculation procedure does not allow T_cforecasting in novel polymer and hence requires updating. Recently Marchionni [12] developed an equation for non-branched perfluoropolyether homo- or co-polymers:

T_C= 200–80(O/C).

The extrapolation of this equation resulted in T_c equal to 200 K (–73°C) for polytetrafluoroethylene (O/C=0), and in T_cequal to 120 K (–153°C) for homopolymer with structure –(CF₂O)–. Below it will be shown that those values differ considerably from our computation results and point to the impossibility of diverging precise functions reasoning only from atomic ratios.

Furthermore A.A.Askadskii proposed a calculation scheme based on the assumption about voluminal dilatation of solid bodies [9,13]. At present such calculation schemes have been developed for quantitative assessment of virtually all polymer properties [14], and the possibility of computer modelling of the synthesis of polymers with designed characteristics has been proved. However, A.A.Askadskii was correct to mention that the applicability of the method decreases as the increments required for calculation accuracy grow in number; and the predictive force of the method may drop to zero, if a novel polymer requires a novel increment to be introduced. Therefore, some polymers e.g., fluoropolymers (never considered by A.A. Askadskii) do not fit in available computational schemes.

We synthesized a series of PFT polymers with different structures of their main and side chains. The analysis of Tc dependence on the length and structure of their triazine rings cross-linking has shown as follows:

1. The introduction of oxygen into PFT polymer side-chain decreases the impact of the main-chain oxygen on the polymer T_c; the said decrease is less obvious for main chains with tetrafluoroethylene oxide links.

2. For polymers with perfluorooxamethylene side-chains only the length of its main-chain influence on the polymer T_c notwithstanding the presence or absence of oxygen in HFPO links.

3. Starting with CF₃O(CF₂O)₂CF₂– radical in side-chain the pattern of T_c dependence on the length of main-chain changes, and T_c decreases with the length of polymer main-chain.

Therefore, the effect of oxygen in main-chain differs from that in side-chain, and oxygen in perfluorooxamethylene group inserted into the polymer side-chain provides the maximal effect.

Following [10], our calculation of T_cin fluoropolymers based on equation (1) with some new increments introduced into it.

Reasoning from the obtained experimental results and taking into account that the contribution of a group does not depend on the nature of adjacent groups only for ideal additivity, and that the best correlation between calculated and experimental results is achieved when group contributions are used instead of those atomic, we made the assumptions as follows:

1. Two K^X_O increment values must be used in the computational scheme: K^X_{O main} for oxygen in the polymer main-chain, and K^X_{O side} for oxygen in the polymer side-chain.

2. The minimal K^X_O value is that of oxygen in perfluorooxamethylene chain.

3. For oxygen surrounded by carbon-containing groups the increment is calculated as the mean of group effects proportional to the number of carbons –C_n–O–C_m– :

4. An additional increment K^X_{O Tr} must be introduced (for triazine ring).

Basing on those assumptions and starting from experimental T_c in synthesized polymers, and using numerical K^X_i values published in [6, 10], we solved the redundant equation system based on (1) and determined new K^X_i values presented in Table 4.

Table 4. Numerical values for K^X_i.

#	Element	Conventional sign	Numerical value (cm3/mole)
1	Oxygen in side oxamethylene chain	KXO side	–3.760
2	Oxygen in HFPO links of main chain	KXO1 main	1.324
3	Oxygen in TFEO links of main chain	KXO2 main	–1.220
4	Triazine ring	KX Tr	32.077

Van der Waals volume for a chain link is calculated as a sum of volume increments ΔV_i shown in Table 5 and taken from published data [10, 15].

Table 5. Increments for van der Waals atomic group volume.

* Calculated by us

Those newly determined increments we used to calculate T_c in synthesized PTF polymers. A comparison between calculated and experimental values shows that both positive and negative deviations and their maximal values are virtually the same (mean square deviation was ±3.1 K), thus confirming the correctness and validity of the calculation scheme.

Figure 1 shows the calculated dependence of T_c on

, that is essentially fits all experimental data.

However, there are some points that poorly fit the calculated curve. They belong to polymers with long perfluoroalkyl side chains. Their deviations of experimental T_c from those calculated with the proposed technique were negative and the quadratic mean deviation was –12.5. For those structures the nature of increments must be revised. It is obvious that in those polymers the impact of their main-chain carbons on T_c differs from that of side-chain carbons.

Fig. 1.

To check our earlier assumptions we calculated T_cin some perfluoropolyethers, and the results are present in Table 6.

Table 6.Calculated and experimental T_C in perfluoropolyethers.

#	Polyether	TC (K) experimental	TC (K)* calculated	Reference
1	–[(CF2CF2O)p(CF2O)q]n– p/q = 0.6¸0.7	142	136.5	[16]
2	–(CF2CF2CF2CF2O)n–	208	221	[17]
4	–(CFCF2O)n– | CF3	201	204.5	NIISK
5	–(CF2O)n–	-	102.5	–

* T_c calculation in polymers with trifluoromethyl side-groups are carried out with K^X_{O2 main} increment, while in polymers without side-chains with K^X_{O side}.

From table 6 one may see that the convergency of experimental and calculated results is not very high, and its mean square deviation is ±7.7. However, taking into account that the method for T_c determination differed from that used by us, and that those polymers are mostly low-molecular, this deviation may be considered as satisfactory. Therefore, we estimated the limit T_cin polyethers, its calculated value in polydifluoromethylene oxide is –170.5°C.

The proposed method for the calculation of glass transition temperature was applied as well in the calculation of T_cof carbochain co-polymers of perfluoroalkylvinyl ethers and vinylidenfluoride [(CH₂CF₂)₃CF(R_f)CF₂]_n manufactured in our institute by the emulsion polymerization. For them the deviation of calculated values from those determined experimentally was somewhat higher than for perfluorooxaalkyltetrazine: ±5.8 K.

Table 7. Structures, T_c, lg Tcand соpolymers of vinylidenfluoride and perfluorovinyl ethers –(CH₂CF₂CH₂CF₂CH₂CF₂CF(Rf)CF₂2)_n–

On the basis of table 7 were derived the dependence of lgT_c on , expressed by the following equation:

or in less complicated form:

This dependence makes it possible to forecast T_c in polymers with the above-mentioned compositions with any perfluorovinyl ether. Similar equations may be derived for any comb-shaped polymers with perfluorooxaalkyl side-chains. E.g., for polymers –[(CF₂CF(R_f)O)₄CF₂O]_n–

For polymers with general formula –[PN(OCH₂R_f)₂]_n–

It fits very well experimental data (mean square deviation does not exceed ±2). The general equation for comb-shaped polymers with perfluorooxaalkyl side-chains is as follows:

Here А and В are constants for this polymer series. Those equations allow sufficient accuracy in the forecasting of T_c in such polymers and rule out complicated calculations using the above algorithm.

As it was already mentioned we have studied experimentally the dependence of T_c in PTF polymers with perfluorooxamethylene side chains on the length of their main chain that contained oxygen in the form of HFPO links, or containing no oxygen. Those were straight-line functions with T_c decreasing with the main chain length. It was interesting to study similar functions for polymers with oxygens in TFEO included into their main chains. Being not able to synthesize such polymers currently we calculated their T_c using the refined calculation scheme. The results are shown in Table 8.

Table 8.Calculated T_C in polymers.

#	Rf	TC (K) calculated
1 2 3 4 5 6 7 8	–(CF2OCF2)2– –(CF2OCF2)3– –(CF2OCF2)4– –(CF2OCF2)5– –(CF2OCF2)6– –(CF2OCF2)7– –(CF2OCF2)8– –(CF2OCF2)9–	139.5 143.5 147 149.5 152 154 156 157.5

From Table 8 one may see for the polymers with TFEO-oxygens the same inverse relationship between the main chain length and T_c, and as the main chain length increases T_c tend to a constant value. It should be noted that for those polymers their T_c is 15÷30K lower than those of similar polymers containing oxygens in OHFP-links of their main chains. It must be due to large contribution of TFEO-link oxygens into the total chain flexibility.

When going from HFPO-linked oxygen to TFEO-linked oxygen K^X_{O main} values change from positive to negative and approach K^X_{O side} of perfluorooxamethylene links, i.e. the main chain becomes less flexible and less different from the side-chain. Taking it into account and having in mind T_c calculated for perfluoropolyethers (Table 6) one may assume that in the case of perfluorooxamethylene main chain its K^X_{O3 main} is equal to K^X_{O side} for perfluorooxamethylene side-chain, i.e K^X_{O3 main} is –3.76. The difference between K^X_{O2 main} and K^X_{O1 main}, is equal to that between K^X_{O3 main} and K^X_{O2 main} , thus confirming to some extent our above assumptions. Reasoning from it we calculated T_c in polymers with perfluorooxamethylene links in their main and side-chains (table 9).

Table 9.Calculated T_C in polymers.

#	Rf	TC (K) calculated
1 2 3 4 5 6 7	–CF2OCF2OCF2– –CF2O(CF2O)2CF2– –CF2O(CF2O)3CF2– –CF2O(CF2O)4CF2– –CF2O(CF2O)5CF2– –CF2O(CF2O)6CF2– –CF2O(CF2O)7CF2–	132 129.5 127.5 126 124.5 123 122

From table 9 one may see that in this case the dependence of T_c on the main chain length, i.e. as the main chain length increases T_c decreases and tends to a constant value. Obviously, the minimal T_cpossible in polymers with above mentioned structures must be about 123 K (–150°C).

We used thus developed calculation scheme to determine T_c in a number of oxygen-containing fluoropolymers, mostly not synthesized yet. Those polymers’ structures and T_c are shown in table 10.

Table 10. Calculated and experimental T_c in oxygen-containing fluoropolymers

From table 10 one may see that the drop of T_c in polymers with long perfluorooxamethylene side-chains is more prominent in polymers with rigid main chain (perfluorocarbons). Similar behaviour was observed in comb-shaped polymers with –CH₂– links in their side-chains [1]. It should be mentioned as well that polymers with flexible main chains and long perfluorooxamethylene side-chains have nearly the same Tcthat and as the number of –CF₂O– links increases their TC tends to Tc of polyperfluorooxamethylene, that is 102.5 K (–170.5°C). The same trend is valid for other polymers but evening-out of their Tc occurs at higher content of –CF₂O– links. Therefore, one may suggest that for any comb-shaped polymers with perfluorooxamethylene links in their side-chains Tc is not less than 102.5K (–170.5°C) that is the minimal Tc value for fluoropolymers.

Examples of vitrification temperature calculation in fluoropolymers

Calculation of Tc in polymer structure as follows:

Van der Waals volume for the polymer link involves five atomic oxygen volumes plus five volumes of –CF₂– groups linked to oxygen and aliphatic carbon; plus two volumes of–CF₂– groups linked to two aliphatic carbons; plus three volumes of ≡CF groups linked to oxygen and two aliphatic carbons; plus six volumes of CF₃ groups linked to aliphatic carbon; triazine ring; plus two volumes of ≡CF groups linked to oxygen, and to aliphatic and aromatic carbons; plus one volume of –CF₂– group linked to aliphatic and aromatic carbons.

The effective volume of repeating link is a sum of corresponding K^X_i values.

T_C = 237.5 K

Calculation of T_c in polymer with the structure as follows:

T_C = 197 K

For oxygen related to triazine ring K^X_O is taken as ½K^X_O for oxygen surrounded of another adjacent group, if K^X_O<0 and 2K^X_O, if K^X_O>0.

Calculation of T_c in polymer with the structure as follows:

K^X_O for oxygen adjacent to the main chain is taken to be equal to ½ of K^X_O for oxygen surrounded of another adjacent group. For соpolymers with similar structures it is ½K^X_h.

Calculation of T_c in polymer with the structure as follows:

For those copolymers we take ½K^X_d.

Calculation of T_c in polymer with the structure as follows:

In order to calculate T_c in such polymers we calculated V_i for group 16.0·10^–24 cm³. The numerical K^X_O value for oxygen connected to two silicons K^X_OSi was calculated from the experimental data on T_c in polymers that was equal to –7.02 cm³/mole.

Therefore, basing on the investigation of the impact of ether bond located in the side- or main chain of PFT polymers on their T_c we have further developed the algorithm earlier proposed by Askadskii and Slonimsky for the computational forecasting of glass transitional temperatures in fluoropolymers and proved its applicability for a large series of polymer structures. Those calculations have shown the principal possibility of synthesis of triazine polymers with perfluorooxamethylene structures in all its fragments with T_c up to 123 K (–150°C) and the synthesis of polyperfluorooxamethylene with T_c equal to 102.5 K (–170.5°C). The minimal achievable T_c in any fluoropolymer is 102.5 K. An empiric equation is proposed for the forecasting of T_c in any comb-shaped polymers with perfluorooxaalkyl side-chains, and its applicability is shown.

The results obtained with the help of the developed calculation scheme made it possible to produce perfluorotriazine liquids with wide temperature range of applicability [18-21]. Those liquids are used for the base in plastic lubricants and antioxidant-anticorrosion additives to perfluoropolyethers and plastic lubricants based on them.

The study was supported financially by the Ministry of Education and Science of the Russian Federation, the State Contract # 02.523.12.3027.

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Recommended for publication by Prof. V. Gubanov

Fluorine Notes, 2011, 78, 7-8