J. MATER. CHEM., 1994,4(5), 741-745 741 Determination of Acid-Base Properties of Solid Materials by Inverse Gas Chromatography at Infinite Dilution A Novel Empirical Method based on the Dispersive Contribution to the Heat of Vaporization of Probes Mohamed M. Chehimi* and Emmanuelle Pigois-Landureau lnstitut de Topologie et de Dynamique des Systemes, Associe au CNRS (URA 34), Universite Paris 7 Denis Diderot, 7 rue Guy de la Brosse, F-75005 Paris, France We introduce a novel empirical method based on AH&,, the dispersive component of the heat of vaporization of probes, to assess the acid-base properties of solid surfaces quantitatively by inverse gas chromatography (IGC) at infinite dilution. In this method, AGa, the free energy of adsorption of probes, is related to AH&.As in the methods of Sawyer, Papirer, Schultz and Donnet we obtain a straight line for alkanes when AGa is plotted vs. For polar probes interacting by both dispersive and specific forces, the experimental data lie above the alkane linear plot. AGP, the specific acid-base contribution to AGa calculated by our new method, matches that determined by the four methods mentioned above. In particular, in the case of self-associated probes (e.g. tetrahydrofuran and ethyl acetate) it yields AG;' values similar to those determined by the method of Donnet et a/., whereas for non-self-associated probes (e.g, chloroform and diethyt ether) AG:' values match those obtained by the methods of Papirer and of Sawyer. A/-&p for polar probes (for alkanes AH&,=AHvap) can easily be determined from the heat of mixing at infinite dilution in apolar solvents, as recommended by Fowkes.The pioneering work of Fowke~l-~ on the role of acid-base interactions in the science and technology of adhesion, mixing and solubility of polymers and other materials have stimulated extensive research work on those topics by several labora- torie~.~As stressed by Fowkes,' the need for methods to assess acid-base properties of materials is urgent. Acid-base inter-actions of materials in the condensed phase are studied by several methods4 including inverse gas chromatography (IGC),6 where 'inverse' means that the stationary phase rather than the mobile phase is the main object of investigation.IGC is very suitable for the characterization of finely divided materials such as polymers, fibres and fillers. In the case of characterization of polymeric materials by means of IGC, the column can either be packed directly with the polymer of interest (powder, beads, fibres, et~.),~or be coated on the inside with the polymer to create a capillary column8 or be packed with small inert spheres coated with a thin polymeric film.g Volatile probe molecules are injected at infinite dilution (zero surface coverage) in order to allow stationary phase-probe molecule interactions only and rule out probe-probe interactions, When semi-crystalline or amorphous polymers are characterized at temperatures above the glass transition temperature, Tg,both surface adsorption and bulk sorption of the probes contribute to the retention times of the probes."*" On the contrary, if IGC experiments are performed at a temperature below Tg,adsorption of the probes on the polymer surface govern their retention times," and sorption by the bulk, which is progressive with time, may be slow enough to be neglected within the timescale of the chromatographic process.12 This constitutes one of the advan- tages of IGC over static methods to study adsorption by polymers.The fundamental retention parameter in GC is the net retention volume of the volatile probe, VN, which corresponds to the volume of the carrier gas required to elute a zone of solute vapour. Of greater importance is the specific retention volume, Vg, which can be defined as V, per unit mass of stationary phase.Depending on the physical state of the packing material at the working temperature, Vg can be related to AGmix or AGa, the free energy of mixing and the free energy of adsorption of the injected probe, respectively. In the case of amorphous or semi-crystalline polymers at a temperature beyond Tg: AG-=RT In [n, In$, +n2 1n$2+~,~n,$,] where subscripts 1 and 2 denote the probe and the polymer, respectively; n,and q5i are the number of moles and the volume fraction of component i, x12is the Flory-Huggins interaction parameter, R the gas constant and T the working temperature. In this expression of AG-, x12can be related to Vgby: x12=ln(273.15 Rv2/PyVgV,)-1+ V1/M2v2 +11-Vl)P?/RT where v2 is the specific volume of the liquid phase (the polymer) and M2 is its molecular weight; V,, Py and B1, are the molar volume, the vapour pressure and the second virial coefficient of the probe in the gaseous state, respectively. For high-molecular-weight polymers, 1/,/M2v2can be neglected in the above expression for x12.When one deals with crystalline solids (inorganic fillers, fibres) or amorphous polymers below their Tg, adsorption phenomena govern the retention of the probes on the material surfaces. Therefore, Vg is related to the surface partition coefficient,K,, defined as the ratio between the concentration of probe in the stationary phase and in the mobile phase, respectively, by: Vg = VN/m =KsAs where m and As are the weight and the specific surface area of the solid of interest, respectively.From Ks, AG, can be derived and expressed as a function of VN by: -AGa=R T In (VN) +C where R is the gas constant, T the working temperature and C a constant which takes into account the weight and the specific surface area of the material, and the standard states of the probes in the mobile and the adsorbed phases. Adsorption of apolar probes (e.g. alkanes) results from London dispersive interactions only, whereas for that of polar probes capable of specific acid-base interactions with the packing material, both London and acid-base interactions contribute to AGa:576 AG, =AG: +AG:~ where AG; and AGtB are the dispersive and acid-base contri- butions to AG,, respectively. However, since only one chroma- tographic signal is recorded for a given polar probe, one has to find a method to distinguish between both contributions to AG,.In the several approaches which were proposed in the literature13-16 to split AGa into its two contributions, AG, [or RTIn(V,)] is plotted uersus a given physicochemical property of the probes. With alkanes a straight line is obtained as shown schematically in Fig. 1. In the case of ‘polar’ probes such as the Lewis acid, chloroform (CHCl,) and the Lewis base tetrahydrofuran (THF), interacting specifically with the solid material, the values of RTln(VN) will lie above the straight line. In Fig. 1,the vertical distance between the alkane reference line and the molecular probe of interest is referred to as: -A G,AB = -(AGa -AG:) =RTIn(VN/VN,ref) where I/N,ref is the net retention volume of a hypothetical reference alkane having the same value of the physicochemical property at the working temperature.The abscissa coordinate on Fig. 1 can be: Tb,the boiling point;13 log(P,), the logarithm of the vapour pressure;14 a(yf)ll2, the product of the cross- sectional area (a)and the square-root of the dispersive contri- bution to the surface energy of the probes [(yt)”2];15 the deformation polarizability.16 In the last approach, Donnet et~2.’~related AG, to London’s equation by: J. MATER. CHEM., 1994, VOL. 4 calculated on the basis of van der Waals models) might not reflect the real situation, especially when specific interactions are concerned.Depending on the nature of the substrate, the probe molecule may have a different geometry” which yields a different contact surface area. In their IGC study of untreated and heat-treated natural Madagascar graphite (high-surface-energy materials), using the approaches of both Papirer14 and Schultz,15 Donnet et all6 found that RTln(VN) values for several probes lay below the dispersive interaction line defined by the alkanes, yielding positive values of ActB. They suggested another AG, data treatment, based on deformation polarizability, for the determination of AGtB. This approach led to negative AGtB values. Donnet et criticized the methods of Schultz” and Papirer14 because in these methods the interaction of an isolated probe with a surface is compared to the probe-probe interaction in the liquid state. However, Donnet et a1.I6 describe the molecular probe-solid interaction by a mol-ecule-molecule interaction.For this reason, their approach may probably not tell the whole story. In this paper we suggest another empirical method for assessing AGtB, where AGa [or RTln(V,)] values are related to AH:,,? the dispersive contribution to the heat of vaporiz- ation of the probes. This approach can be understood as follows. First, according to Trouton’s rule: where LVa?is the latent heat of vaporization and Tb the RTIn(V,)+C =K(h~~)~~~~l~,~(hv~)~~~~l~,~boiling point. where C is a constant, hvi the ionization potential of the ith interacting material, cto the deformation polarizability and K a constant which takes into account the permittivity in vacuum, the distance of adsorbate-adsorbent interaction and Avogadro’s number. S and L refer to solid and liquid.The main interest of this method lies in the fact that the probes are characterized by an intrinsic property derived from London forces. We have used the approach of Saint Flour and Papirer14 to study the dispersive and acid-base properties of conducting polypyrrole (PPy) Panzer and Schrei ber17 have recently compared the methods of in their study of polycarbonate surfaces and found similar AGtB results for each polar probe. They concluded that the approach of Sawyer and Brookman13 was the most convenient since Tb of most widely used probes are readily available in the literature.Nevertheless, Schultz et a2.’s15method is attractive since the parameter characterizing the probe contains yf. Such an approach was actually sought by Gray1* a decade ago. However, the major difficulty of this method lies in the determination of a. Conceptually, the value of a (usually physicochemical property Fig. 1 Method for the evaluation of AG,AB between polar probes and the solid stationary phase: 0,alkanes; H,polar probe Secondly, the Clausius-Clapeyron equation states that AH,,, and log(P,) are related by: log(Po)= -AH,,,/RT+constant At this stage, one is tempted to correlate AGa [or RTln(V,)] with AH,,, since both equations involve AH,,,.However, in the case of self-associated liquids, Trouton’s rule does not hold since the ratio is significantly higher than 80 J K-’ mol-1.20 Moreover, Fowkes’ has shown that, for self-associated probes, AH,,, includes a significant acid- base contribution. It obviously follows that these interactions contribute also to log(P,) and Tb. We thus suggest that RTln(VN) be related to AHtaP rather than AHvap, since the former reflects a dispersive property of the injected probe. After a brief account of the method for the evaluation of AH:ap, we shall apply our approach to the retention data of apolar and polar probes injected in chromatographic columns packed with chloride-doped polypyrrole (PPyCl). The ‘AHtaP’approach is applicable to PPyCl since this polymer is not soluble in any common solvent and not fusible.Added to this, PPyCl is a very rigid material and does not soften at all at the column temperature we have used. Thus the retention data are due solely to the adsorption phenomena of the molecular probes. Experimental Chemical Synthesis PPyCl powders were chemically synthesized by oxidative polymerization by the method of Rapi et at 0 “C using urea as a buffer. The concentrations of pyrrole (Aldrich) and oxidizing agent, FeCl, (Prolabo) were 0.1 mol 1-1 and 0.3 moll-’, respectively. The black PPyCl powder was washed with doubly distilled water, dried in a vacuum desiccator and then sieved to less than 100 pm. J. MATER. CHEM., 1994, VOL. 4 IGC Stainless-steel columns of 1/8 in ( 1 in =2.54 cm) outer diam- eter (od) and 30cm length were packed with ca.160mg of PPyCl powder. A gas chromatograph (Girdel 330) fitted with a flame ionization detector was used. CH, was the non-interacting marker and helium was the carrier gas. The flow rate was 16 ml min-l. The oven temperature was 53 "C as measured by a digital thermometer. The injector and detector tempera- tures exceeded that of the column by ca. 20 "C only to avoid temperature gradients at the inlet and outlet of the column. The columns were conditioned at 110 "C for 15 h. Probe molecules were injected manually by a Hamilton gas-tight syringe at extreme dilution. The signals were recorded with a Delsi 21 digital recorder and the retention times determined graphically according to the method of Conder and Young.12 Results and Discussion In this section, we first recall how we evaluated AH:,, values of the injected probes and then we compare the various methods which can be used to calculate AG2B values.Evaluation of AHLpValues Fowkes has suggested an easy method to split AHvapinto its dispersive and acid-base contributions for self-associated liquids using AHZix, the limiting heat of mixing at infinite dilution in hexane or cyclohexane (apolar solvent^):^ A U:,, =(VP-AHZix+A U,,,)'/4 Vd2 (1) where V is the molar volume of the probe, 6 the solubility parameter of the apolar solvent, AU,,, is the total energy of vaporization of the probe and AU:,, its dispersive component.Once AUd is determined by eqn. (l), one can calculate AH:ap, A Ut$:acid-base contribution to AU,,,) and the degree of self-association (%SA): (i) AH:,^ =AU:,, +RT (ii) AU:?, =AU,,, -AU:,, and (iii) %SA=(AU~&/AUV,,)lOO% We have used the values of AH:ap published by Fowkes5 for the polar probes. Those for 1,4-dioxane (DXN) and CH2C12 were lacking. They were determined as follows. Fig. 2 shows the heat of mixing of DXN and CH2C12 in hexane us. the molar fraction x at 25 "C. AHZix is the limiting slope at 18001 1 1200' c 1 .I -5 9001El -I2 600 aJ= 3001a, I 0.0 0.1 0.2 0.3 0.4 0.5 0.6 mole fraction of probes in hexane Fig. 2 Heats of mixing of 1,4-dioxane (0)and of CH2C12 (A)into hexane uemm the mole fraction, at 25 "C. The variations of the heats of mixing with x were fitted by: H(CH,C12)= -5741.2x2+ 5845.1~ 9164.9~~-6070.1~~ -0.256 and H(dioxane)= 3893.1x4+ 136.1~~ -9121.3x2+7197.8x-O.438 x=O.The heats of mixing were reported by Christensen .~et ~1 Using~ AHZx in eqn. (l),the determination of AH:,, for DXN and CH2C1, is straightforward. The values of AH:!, and AH,,, for alkanes and polar probes are reported on Table 1. For DXN, AH:,, differs significantly from AH,,, and yields a percentage of self-association of 19%. This is quite surprising for a 'pure' Lewis base for which Gutmann's acceptor number is negligibly CH,CI, is self-associated to the extent of 13% although it was expected to have a low %SA comparable to those of CHCI, arid CCl,.5 However, such a %SA is in line with a recent IR study which demonstrated that CH,Cl, dimerizes by double hydrogen bonding in inert solvents.26 Evaluation of AGF We compare six methods of evaluating AGtB, where R T ln(V,) values are related to the abscissa coordinates which are labelled as follows: I, AH:,,; 11, AH,,,; 111, T,,; IV, log(Po); V, a(~d,)l'~;VI, (~V)~/~CX,~O~~.Table 2 reports RT ln(VN) values for alkanes and polar probes adsorbed on PPyCl powder at 53 "C. The probes are indeed adsorbed and not absorbed in the PPyCl bulk, as evidenced by the heats of adsorption which vary in the range of 25-43 kJ mol-l on going from hexane to nonane7" and are thus comparable to the AH,,, range for these alkanes.Following the work of Dorris and Gray27 on poly(ethy1ene terephtalate), we found for AG2H2,the free energy of adsorption of a methylene group in the alkane series, a value of 2.7 kJmol-l. This value is almost equal to 2.76 kJmol-l which is that of AGZH2, the free energy of liquefaction of a methylene group in the same series. Fig. 3 shows a plot of RT ln(VN) us. AH:,, for probes Table 1 Values of AH:ap and AH,,, for alkanes and polar probes probe AH:,,)CJ mol-' AH,,,/W mo1-l hexane 31.5 31.5 heptane 36.5 36.5 octane 41.5 41.5 nonane 46.4 46.4 decane 51.4 51.4 CCl, 31.9 32.4 CHC1, 30.4 30.8 CH2C1, 27.8" 3 1.7' ether 25.8 27.4 DXN 29.4" 35.8b THF 23.3 30.9 EtAc 29.3 34.9 AH,,, for n-alkanes were taken from ref.23; AH,,, and AH$,, for other probes from ref. 5. 'AH:,, calculated according to ref. 5 and using the heat of mixing of DXN and CH2C12 in hexane from ref. 22. bFrom ref. 24. Table 2 Values of RT In(&) for alkanes and polar probes adsorbed on PPyCl at 53 "C probe RT In(V,/ml min-l)/kJ mol-' hexane -1.67 heptane 0.97 octane 3.96 nonane 6.35 CCI, -0.11 CHCI, 3.24 CH2Cl, 4.52 ether -0.86 DXN 7.07 EtAc 6.25 THF 5.00 J. MATER. CHEM., 1994, VOL. 4 81 -l1 6t 0 Fig. 3 Plot of RTln(V,) us AH:a, for alkanes and polar probes adsorbed on PPyCl at 53 "C: 0, C,-C,; a, DCM; 0, CHCI,; t,CCl,; A,ether; 0,THF; V,EtAc; +, DXN adsorbed on PPyC1. It is very interesting to note that for alkanes a linear correlation is obtained, as with the previously published methods (111-VI). The alkane line has the same slope as that determined using AHvap,since AH:ap =AHvap for the alkane series.For polar probes interacting specifically with the substrate, their corresponding markers are above the 'dispersive' line defined by the alkanes. Table3 lists %SA and AGtB values for the polar probes determined by methods I-VI on the basis of RTln(VN) values in Table 2. Table 3 shows that: (i) AGtB values calculated by our new method (I) are included in the range of those determined by all other methods (11-VI); (ii) for any polar probe, the AGkB value obtained by method VI is invariably greater than those of methods I-V; (iii) with the exception of EtAc, methods I, I11 and IV lead to AGF values invariably greater than those of method V (this is in line with a recent IGC study of birchwood meal by methods IV and V7d); (iv) for the poorly self-associated liquids (CHC13, CC14 and ether) we obtain AGtB values similar to those with methods 11-V.This holds also for CH2C12, although it has a higher %SA. (v) As far as probes of higher %SA are concerned (DXN and THF), AGtB values are comparable to those obtained by method VI but significantly greater than those determined by methods 11-V, since in these methods the self- association aspect of the probes is ignored. Although in method V the self-association character is considered, one has to keep in mind that for the polar probes used in this work Jyt NN JyL. Moreover, the experimental evaluation of a using apolar reference solids31 may lead to values which differ from those obtained in the real situation involving a polar adsorb- ent.(vi) When we applied the approach of Donnet et a1.16 to CCl,, we surprisingly determined a very high value of -Table 3 Values of AGf' for polar probes adsorbed on PPyCl at 53 "C and determined by several methods -AG,AB/kJ mol-' probes %SA I I1 I11 IV v VI CCl, 1.6 1.4 1.1 1.1 0.8 0.0 4.0 CHCI, 1.6 5.5 5.3 5.8 5.7 4.1 8.3 ether 6 3.9 3.0 4.4 4.2 3.3 5.4 CH,Cl, 13 8.2 6.1 9.0 8.9 7.7 13.7 Et Ac 18 9.1 6.1 7.2 7.0 8.2 11.1 DXN 19 9.9 6.4 5.7 5.5 4.0 10.5 THF 27 11.1 7.0 7.0 6.9 6.8 12.5 MeJhods I11 and IV: Tb and log(Po) were from ref.24. Method V: a in A' from ref. 28; yt from ref. 29 for alkanes, from ref. 28 for THF, ether and EtAc, from ref. 30 for halogenomethanes and DXN. Method VI: (h~)'/~a,lO~~values in C3/21/2rn-l/' from ref. 16 except for DXN, CHzClz and CCl, which were calculated by us according to ref. 16. ~ 14 Ii 7 E. 0 $61 8 0 *+ iz 0.8 ~ D I I -2L CCI4 CHCl3 ether EtAc THF-self-associated probes Fig. 4 Comparative evaluation of AG?, by six different methods, for polar probes adsorbed on PPyCl: 0,AH:,,; U, AH,,,; A, log Po; + a(y$)'; Tb; 0 (hv)'ao x AGtB (4.0kJmol-'), whereas it has a value in the range 0-1 kJ mol-I by methods 111-V. Obviously, this is a great discrepancy, especially in the case of the quasi-neutral CCl, for which we obtain a 'reasonable' AGtB value (-1.4 kJ mol-l).Although this probe was mentioned in their paper,16 Donnet et al. did not report any AGtB for CC14 adsorbed on untreated and heat-treated Madagascar graphite. Generally, Table 3 clearly shows that for chloromethanes, AGtB values by method VI deviate significantly from those determined by all other methods. Fig. 4 summarizes this comparative study by a plot of AGtB determined with the six methods for some polar probes characterized by %SA and adsorbed on PPyCl at 53 "C. The results obtained with PPyCl and discussed above fall in the most frequent situation of polar probes data lying above the dispersive alkane line. However, some system^'^.^^ yield positive AGtB values.In other words, the RTln(V,) values for polar probes lie below the reference line. Although Donnet et suggested the 'deformation polarizability' method to overcome this shortcoming, one could question these observations when the classical approaches are applied as follow^.'^-^^ Is this due to the method applied to the raw retention data or is there a real thermodynamic effect, like perhaps repulsion forces?33 Is the use of alkanes, for sub- tracting the London contribution to AGa, a universal method or perhaps should IGC users choose perfluoroalkanes to account for dispersive interaction^?^^^^' It has been shown that n-alkanes may diffuse in porous and lamellar materials but not bulky This phenomenon may induce an additional mechanical retention which 'raises' the alkane reference line, thus leading to positive AGtB for the polar probes.A key to this diffusion may be found in the determi- nation of indexes of morphology as suggested by Papirer et ~ 1 . ~ ~ Conclusions We have introduced a novel empirical method for the quanti- tative assessment of acid-base gas-solid interactions by means of IGC and based on AHtap, the dispersive contribution to the enthalpy of vaporization of probes. It is shown not only that the AH:ap approach is linked to those of Sawyer and of Papirer but, more importantly, takes into account the self- association character of the polar probes, as recommended by Fowkes.' For polar probes of low percentage of self- association (%SA) our approach yields AGtB values compar- able to those obtained by the classical methods of Sawyer, Papirer and Schultz.On the other hand, it yields AGtB values matching those obtained by the method of Donnet et al., when applied to probes of high %SA. In the special case of J. MATER. CHEM., 1994, VOL. 4 745 chloromethanes, our method leads to AG," values which 10 A. Exteberria, J. Alfageme, C. Uriarte and J. J. Truin, disagree with those obtained by Donnet's method. At this stage it is reasonable to restrict our method to temperatures close to ambient since AHtaPis calculated using calorimetric measurements at 25 "C.In the same manner as the IGC approach of Gray18 for determining the dispersive 11 12 13 J.Chromatogr., 1992,607,227. J. E. Guillet, M. Romansky, G. J. Price and R. van der Mark, ref. 6, ch. 3. J. R. Conder and C. L. Young, in Physicochemical Memurements by Gas Chromatography, Wiley-Interscience, New York, 1979. D. T. Sawyer and D. J. Brookman, Anal. Chem., 1968,40,1847. contribution to the surface energy of solids, our new method of estimating AGtB is only applicable to adsorption phen- omena and it should not be used when strong polymer bulk diffusion of the probes is suspected. Given that, the 'AH:ap' method of determining the acid-base properties of polymers 14 15 16 17 C. Saint Flour and E. Papirer, J. Colloid Interface Sci., 1983, 91,69. J. Schultz, L. Lavielle and C. Martin, J.Adhesion, 1987, 23,45. J. B. Donnet, S. J. 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