The magnitude of the interactions between two phases may be deduced from results collected by various experimental techniques. One of them is Inverse Gas Chromatography (IGC). IGC is an extension of conventional gas chromatography in which a non-volatile material to be investigated is immobilized on a column. Parameters determined during IGC experiments may be successfully used in the characterization of polymers and their blends, composites and fillers as well as other materials, quantification of the interactions between the components of a polymer's mixture including the interactions between polymeric components and filler surface. Authors propose to express the magnitude of filler–polymer interactions by using the modified procedure of the determination of Flory–Huggins χ23′ parameter. It was calculated from retention data of test solutes collected during inverse gas chromatographic experiments. Here, this method was applied for characterization of a series of poly(ethylene glycol) 10,000 (PEG) and poly(L-lactide) (PLA) (59,000) compositions with Aerosil® 200 V (AR_200). The usefulness of some methods to eliminate dependence of χ23′ on the type of test solute was examined and discussed.
Introduction
Polymer blends are a new class of materials needed to replace heavy metal alloys. Blending of polymers is a fast and inexpensive route to obtaining this class of materials [1].
Composite materials (polymers with inorganic fillers) play an important role in many fields of science. Addition of filler lowers the cost and also improves the tensile strength of the base resin. The strength of the interactions between components of the composite is the key factor in polymer materials characterization. Filler content, chemical characteristics of the components, and filler characteristics significantly influence the rheological and mechanical properties of the polymer composites. Also any change in the polymer–filler interactions affects the properties of the composition.
Anzeige
A variety of experiments are being used to determine material compatibility. Only a few techniques can give quantitative information about the change of free energy when mixing two components. One of them is inverse gas chromatography [2]. During the years this technique has become an accurate, reliable, and fast method for physicochemical characterization of polymer systems. The properties of the examined material are deduced from the retention data of test solutes of different chemical natures. Retention parameters depend on the magnitude of interactions between test solutes and examined material, e.g. a polymer blend playing the role of the stationary phase in a chromatographic column. Retention data are further used for calculation of physicochemical characteristics of various materials.
The usefulness of IGC for determining polymer–small molecule interactions is well established. Experimentally determined retention parameters are easily recalculated into Flory–Huggins parameters, using the equation [3]:
where: 1 denotes the solute, and 2 or 3 denotes the examined material (polymer or filler, accordingly). M1 is the molecular weight of the solute; p1o is the saturated vapour pressure of the solute, and B11 is the second virial coefficient of the solute. Vi is the molar volume; ρ
i
is the density. R is the gas constant, and V
g
is the specific retention volume.
In the case of the mixture (e.g. polymer–filler composition) Eq. (1) could be rearranged into [4, 5]:
Here, the second subscript of Vg identifies the nature of the column.
To obtain χ23′ for a polymer blend or composition utilizing IGC, χ12∞ values for all components have to be known. Therefore, three columns are usually prepared: two for single components and the third one for a composition of the two components used. A further three columns containing different compositions of components can also be prepared if the effect of the weight fraction of the mixture on the examined property needs to be explored. These columns should be studied under identical conditions of column temperature, carrier gas flow rate, inlet pressure of the carrier gas, and with the same test solutes [8].
A large positive value indicates the absence of or negligible interactions between components; a low value indicates favourable interactions, while a negative value indicates strong interactions. Values of Flory-Huggins χ23′ parameter depend on the chemical structure of the solute, and it is a common phenomenon, although not allowed by the theory [9]. It has been interpreted as a result of preferential interactions of the test solute with one of two components. Deshpande et al. [10] applied this technique for the determination of thermodynamic interactions between components of a mixture of polymer and nonpolymeric compound. Su et al. [11] used this technique to measure the interaction parameter of poly(vinyl chloride) (PVC) and dioctyl phthalate as a plasticizer to study their compatibility. Later, this method was also used to measure the compatibility of polymer blends. However, many studies have shown that the polymer-polymer interaction parameters determined by this technique depend on the probes used. Hsu and Prausnitz and Patterson and co-workers suggested that the compatibility of polymeric components in solution should reflect not only the interaction between the components themselves, that is, χ23′, but also the difference in the strengths of the polymer-probe interactions, that is: Δχ = |χ12 − χ13|. They called it the Δχ effect, and a large Δχ value, in addition to a high χ23′ value, suggests incompatibility.
Deshpande and Farooque observed probe dependency and tried to develop a method to evaluate probe-independent interactions [12].
Milczewska and Voelkel [7] discussed some of the methods of evaluating probe-independent interaction parameters. One of the solutions may be a procedure proposed by Zhao and Choi [4, 5]. The authors proposed to use ‘common reference volume’ (Vo), which eliminates the problem. For the reference volume, they used molar volume of the smallest repeated unit of polymer. Their definition of χ differed form the traditional definition by the ratio of the reference volume to the probe volume (Vo/V1). When a common reference volume was used, the data conformed to the ternary version of the Flory-Huggins lattice theory, and unique χ23 values were obtained.
Zhao and Choi demonstrated that by selecting a proper common reference volume for analyzing IGC data, one can yield reliable solvent-independent χ23, so long as the solvents used satisfy the zero Δχ criterion.
Flory-Huggins parameter for blends can be calculated from the equations:
Equation (5) predicts that a plot of χ1m versus (φ2 ⋅ χ12 + φ3 ⋅ χ13) will give a straight line with a slope of 1 and an intercept of − φ2 ⋅ φ3 ⋅ χ23′.
J. C. Huang [13] and R. Deanin [14] rearranged Eq. (5) into the following form:
The polymer-polymer interaction term can be determined from the intercept at \( \left(\frac{\varphi_2\cdot {\chi}_{12}+{\varphi}_3\cdot {\chi}_{13}}{V_1}\right)=0 \). This modification provided smaller standard deviations for the slope and the polymer–polymer interaction parameter [15]. J. C. Huang [16] presented some of the constraints of the models used. He noticed that the IGC technique couldn’t be used in immiscible systems, because the equation of the parameter was derived based on the assumption of miscible components (blends). However, two different monomers can be brought together into a one-component system by copolymerization. So the interaction parameters between solutes and copolymers should follow a trend intermediate between the two homopolymers.
Flory-Huggins parameters from basic procedures for such types of systems were calculated successfully [17, 18].
The aim of this work was to present the possibility of applying the thermodynamic relations determined by IGC for polymer blends to polymer–inorganic filler mixtures. The authors proposed to use Zhao-Choi’s and Huang’s procedures to determine interaction parameters in polymer–filler systems.
Materials
IGC experiments were used to examine the interactions of polymer–filler systems containing poly(ethylene glycol) (PEG) (average molar mass ∼10,000 g⋅mol−1) and poly(L-lactide) (PLA) (55,000 g⋅mol−1). Polymers (supplied from Sigma Aldrich) were mixed with hydrophilic fumed silica – Aerosil®200 V (A) [19] (delivered from Evonik Industries). Detailed compositions of tested formulations are shown in Table 1.
Table 1
Compositions and used symbols
Used symbol
Aerosil—PEG
Aerosil—PLA
A-PEG/A-PLA
Weight fractions [g]
Weight fractions [g]
0-1
0.00 - 2.00
0.00 - 1.00
1-1
1.00 - 1.00
0.50 - 0.50
2-1
1.35 - 0.65
0.68 - 0.32
3-1
1.50 - 0.50
0.75 - 0.25
4-1
1.60 - 0.40
0.80 - 0.20
5-1
1.66 - 0.34
0.88 - 0.12
Experimental conditions
Measurements were carried out with the use of Chrom5 (Kovo, Czech. Rep.) gas chromatograph equipped with FID. Teflon columns, 50 cm × 0.3 mm I.D., were packed with the support coated with polymer or filled polymer. Polymers, filler and compositions were mixed with glass beads at 1 wt% loading. The following compounds were used as test solutes: pentane (C5), hexane (C6), heptane (C7), octane (C8), nonane (C9), methylene chloride (CH2Cl2), chloroform (CHCl3), ethyl acetate (EtAc), acetonitrile (ACN), ethanol (EtOH), and 1,4-dioxane (DIOX). Dry helium with a flow rate of 15 ml/min was used as a carrier gas. The investigated materials were mixed homogeneously with the glass beads. Measurements were carried out at infinite dilution, which means that a very small amount of the test solutes was injected onto the chromatographic column filled with the examined material. All columns were conditioned overnight at the flow rate and temperature used later during IGC experiments. Retention parameters of test solutes (retention time and volume) were used to calculate values of physicochemical parameters characterizing the examined materials.
Results
Flory-Huggins χ1m∞ and χ23′ parameters
Values of Flory-Huggins parameter χ1m∞ were calculated from Eq. (2) for all investigated compositions. All the data are positive, but in all systems we can find solute for which the composition is slightly miscible (Figs. 1 and 2). The strongest interactions with test solute were observed for compositions A-PEG 1-1 and A-PLA 2-1. Aerosil also strongly interacts with the test solutes – significantly with ethyl acetate. Lower values than for alkanes were obtained for the polar probes. The best solvent (the strongest solvent–composition interaction) for both series of compositions is ethyl acetate.
Fig. 1
Values of χ1m∞ parameter for compositions with PEG at 353 K
Fig. 2
Values of χ1m∞ parameter for compositions with PLA at 353 K
×
×
Flory-Huggins parameter χ23′ indicates the magnitude of interactions between components of the composition. In compositions with PEG (Fig. 3), for almost all proportions, negative values of χ23′ were obtained. In a series of A-PLA (Fig. 4) compositions, only the 1-1 Aerosil-PLA mixture is characterized by some negative χ23′ values. The lowest values of χ23′ are obtained for polar probes. Column temperature also influences the values of determined parameters. χ23′ values for alkanes decreased with increasing temperature, but increased for polar probes.
Fig. 3
Values of χ23′ parameter for A-PEG 4-1 composition
Fig. 4
Values of χ23′ parameter for A-PLA 1-1 composition
×
×
Because of χ23′ probe dependency, we used the procedures of Zhao-Choi and Huang for calculation of solute-independent χ23′.
Zhao-Choi procedure
For all compositions, values of the parameter χ23′ were calculated from the procedure of Zhao-Choi (Eq. 4 and 5). As a ‘reference volume’, we used molar volume of repeated unit of polymers (in the case of PEG, it was Vo = 55.8 and, for PLA Vo = 74.5 [cm3/mol]). Results are presented in the Tables 2 and 3.
Table 2
Values of χ23′ calculated from Zhao-Choi procedure for PEG composites
\( {\chi}_{23}^{\mathit{\mathsf{ZC}}} \)
353 K
363 K
373 K
A-PEG 1-1
−1.26E-03
−8.25E-04
−6.28E-04
A-PEG 2-1
−8.79E-04
−3.23E-04
−1.43E-04
A-PEG 3-1
1.26E-04
1.79E-05
−3.95E-04
A-PEG 4-1
4.66E-04
9.86E-04
1.67E-03
A-PEG 5-1
−9.15E-04
−4.66E-04
3.05E-04
Correlation coefficient higher than R2 = 0.94
Table 3
Values of χ23′ calculated from Zhao-Choi procedure for PLA composites
\( {\chi}_{23}^{\mathit{\mathsf{ZC}}} \)
353 K
363 K
373 K
A-PLA 1-1
−5.24E-04
−5.91E-04
−3.90E-04
A- PLA 2-1
−8.46E-04
−8.60E-04
−6.31E-04
A- PLA 3-1
−8.06E-04
−9.13E-04
−6.45E-04
A- PLA 4-1
−2.69E-05
−4.03E-05
1.34E-05
A- PLA 5-1
−2.69E-04
−2.15E-04
7.93E-04
Correlation coefficient higher than R2 = 0.955
Almost all \( {\chi}_{23}^{\mathit{\mathsf{ZC}}} \) values are slightly negative (with the exceptions of A-PEG 3-1 and 4-1), which may suggest the existence of strong interactions in these compositions. \( {\chi}_{23}^{\mathit{\mathsf{ZC}}} \) value increases with the increasing of the filler content in A-PEG compositions. \( {\chi}_{23}^{\mathit{\mathsf{ZC}}} \) values are smaller for A-PLA series than for A-PEG composites. The weakest interactions in A-PLA composities were found for 5-1 and 4-1; the highest value of \( {\chi}_{23}^{\mathit{\mathsf{ZC}}} \). The strongest interactions was shown for A-PLA 3-1 composite.
Huang’s procedure
For all investigated compositions we also calculated χ23′ parameterrs from the J-C. Huang procedure (Eq. 6). The obtained values are presented in the Tables 4 and 5.
Table 4
Values of χ23′ calculated from Huang procedure for PEG composites
\( {\chi}_{23}^{\mathit{\mathsf{H}}} \)
353 K
363 K
373 K
A-PEG 1-1
−1.88E-05
−1.41E-05
−1.17E-05
A-PEG 2-1
−2.80E-05
−2.18E-05
−1.72E-05
A-PEG 3-1
−3.32E-05
−2.59E-05
−1.17E-05
A-PEG 4-1
−4.21E-05
−3.27E-05
−2.73E-05
A-PEG 5-1
−4.89E-05
−3.95E-05
−3.34E-05
Correlation coefficient higher than R2 = 0.958
Table 5
Values of χ23′ calculated from Huang procedure for PLA composites
\( {\chi}_{23}^{\mathit{\mathsf{H}}} \)
353 K
363 K
373 K
A-PLA 1-1
−5.23E-07
−4.09E-07
−2.95E-07
A- PLA 2-1
−6.59E-07
−4.55E-07
−3.86E-07
A- PLA 3-1
−2.27E-07
−4.55E-07
−3.86E-07
A- PLA 4-1
−1.45E-06
−1.09E-06
−1.30E-06
A- PLA 5-1
−1.41E-06
−1.61E-06
−4.09E-07
Correlation coefficient higher than R2 = 0.981
For both series of compositions we obtained negative values of the \( {\chi}_{23}^{\mathit{\mathsf{H}}} \) parameter. Compositions with PEG were characterized by smaller \( {\chi}_{23}^{\mathit{\mathsf{H}}} \) values than A-PLA. The lowest values were obtained for A-PEG 5-1 and A-PLA 5-1 compositions. In the Huang procedure, increasing the amount of the filler caused a decrease of the \( {\chi}_{23}^{\mathit{\mathsf{H}}} \) values.
The arrangement of the examined compositions according to the procedures proposed by Zhao-Choi and Huang is different. This is probably due to varying the volume used as ‘reference’ for calculation of χ1m.
From values of χ23′ calculated on the base of “solute-independent” procedures, we can state that the best composition with the highest interaction between components is A-PLA 3-1 composition (the lowest value of \( {\chi}_{23}^{\mathit{\mathsf{ZC}}} \)).
From \( {\chi}_{23}^{\mathit{\mathsf{H}}} \) values, it follows that the strongest interaction occurred for the A-PEG 5-1 composition.
In literature Flory-Huggins interaction parameter χ23 is usually presented as a ratio \( {\scriptscriptstyle \raisebox{1ex}{${}^{\chi_{23}}$}\!\left/ \!\raisebox{-1ex}{${}_{{\mathit{\mathsf{V}}}_2}$}\right.} \) to discount the reference volume value. In our case, values of \( {\scriptscriptstyle \raisebox{1ex}{${}^{\chi_{23}}$}\!\left/ \!\raisebox{-1ex}{${}_{{\mathit{\mathsf{V}}}_2}$}\right.} \) for both procedures are presented in Figs. 5 and 6 (Zhao-Choi) or Figs. 7 and 8 (Huang).
Fig. 5
Values of \( {\scriptscriptstyle \raisebox{1ex}{${}^{\chi_{23}}$}\!\left/ \!\raisebox{-1ex}{${}_{{\mathit{\mathsf{V}}}_2}$}\right.} \) calculated from Zhao-Choi procedure for PEG compositions
Fig. 6
Values of \( {\scriptscriptstyle \raisebox{1ex}{${}^{\chi_{23}}$}\!\left/ \!\raisebox{-1ex}{${}_{{\mathit{\mathsf{V}}}_2}$}\right.} \) calculated from Zhao-Choi procedure for PLA compositions
Fig. 7
Values of \( {\scriptscriptstyle \raisebox{1ex}{${}^{\chi_{23}}$}\!\left/ \!\raisebox{-1ex}{${}_{{\mathit{\mathsf{V}}}_2}$}\right.} \) calculated from Huang procedure for PEG compositions
Fig. 8
Values of \( {\scriptscriptstyle \raisebox{1ex}{${}^{\chi_{23}}$}\!\left/ \!\raisebox{-1ex}{${}_{{\mathit{\mathsf{V}}}_2}$}\right.} \) calculated from Huang procedure for PLA compositions
×
×
×
×
For values obtained from the Huang procedure for both compositions, we can observe linear dependency from the amount of filler; for calculations from Zhao-Choi that dependence isn’t linear.
The influence of the temperature was also observed. For A-PEG compositions an increase of the temperature causes an increase of the values of Flory-Huggins parameter χ23′; whereas for A-PLA compositions the strongest interaction (the smallest χ23′ values) were observed in the middle temperature independently from calculation procedure.
Which procedure is "better”? For those kinds of material, i.e., compositions of polymer with inorganic filler Huang’s method seems to be more suitable. Values of \( {\scriptscriptstyle \raisebox{1ex}{${}^{\chi_{23}}$}\!\left/ \!\raisebox{-1ex}{${}_{{\mathit{\mathsf{V}}}_2}$}\right.} \) calculated by the Huang method for both series of compositions are smaller than those obtained from the Zhao-Choi equation.
This is more clear for interpretation of the strength of interaction (values ∼0 may suggest existence of interaction or not). Linear dependence of \( {\scriptscriptstyle \raisebox{1ex}{${}^{\chi_{23}}$}\!\left/ \!\raisebox{-1ex}{${}_{{\mathit{\mathsf{V}}}_2}$}\right.} \) values on the amount of the components is an additional advantage. It may facilitate the prediction of the magnitude of interactions in future investigations. However, the existence of such relationship should be confirmed for a larger group of investigated complex materials.
Results obtained by using standard and “solute-independent” Huang’s procedures indicated strong interactions between components, as negative values of χ23′ were found. Therefore, we suggest the use of the parameters determined by Huang’s method in drawing conclusions on the properties of the examined complex polymeric systems.
Conclusion
The IGC method was used for estimating the magnitude of interactions between the components of polymer compositions. Flory-Huggins parameters for polymer–filler systems were calculated using standard and “solute-independent” methods. Negative values of Flory-Huggins interaction parameter χ23′ were found for almost all examined mixtures, which indicates significant interactions of the components used. It has been found that χ23′ values depend on the nature of the test solute used in the IGC experiment. Stronger interactions were observed for the A-PEG composition (lower values of χ23′). Application of Zhao-Choi and Huang procedures leads to elimination of solute dependence of χ23′. Values \( {\scriptscriptstyle \raisebox{1ex}{${}^{\chi_{23}}$}\!\left/ \!\raisebox{-1ex}{${}_{{\mathit{\mathsf{V}}}_2}$}\right.} \) obtained from Huang procedure for both compositions depend linearly on the amount of filler. By using \( {\scriptscriptstyle \raisebox{1ex}{${}^{\chi_{23}}$}\!\left/ \!\raisebox{-1ex}{${}_{{\mathit{\mathsf{V}}}_2}$}\right.} \) values, one may follow the changes in the magnitude of interactions between the components of the composition resulting from the changes of filler properties, its amount and temperature.
Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.
