Diffusion of Aromatic Isomers in Acetone: An Investigation on the

Nov 8, 2017 - By taking into account of the small corrections for the differences in molecular shape and steric hindrance between the o- and m-isomers...
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Diffusion of Aromatic Isomers in Acetone: An Investigation on the Effects of Intramolecular and Intermolecular Hydrogen Bonding T. C. Chan,* W. Y. Tang, N. W. Chang, and Cherie H. C. Chan Department of Applied Biology and Chemical Technology, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong ABSTRACT: Limiting mutual diffusivities of o- and m-isomers of methylaniline, nitroaniline, nitrophenol, and aminophenol were measured in acetone at 298.2 K by the Taylor dispersion method. The data reveal that all of the o-substituted solutes capable of intramolecular hydrogen bonding diffuse faster than their m-counterparts without such bonding. By taking into account of the small corrections for the differences in molecular shape and steric hindrance between the o- and m-isomers that can form solute−solvent complexes, the net effects of intramolecular hydrogen bonding were uncovered to render the o-isomers greater in diffusivity by 3−15% as compared to their m-isomers in this study. For aromatic amines and phenols diffusing in acetone, the overall effects of intermolecular hydrogen bonding on diffusivity were ascertained by comparing the available diffusivity data of the associated aromatic solutes with those of the nonassociated ones. The intermolecular effects that cause solutes to diffuse slower were found to vary from approximately 12−39% in the present work. The results indicate that both of the opposite intra- and intermolecular effects are significant. In addition, the quantified effects were analyzed to show that they are closely related to the nature and position of the functional groups contained in the aromatic solutes, including those that are unable to form hydrogen bonds with acetone. A relation that can correlate the diffusivities of the hydrogen-bonded aromatic amines and phenols in acetone with the overall acidities of the compounds is also presented.

1. INTRODUCTION Hydrogen bonding (H-bonding) is commonly found in biological and chemical systems, and diffusion of molecules is known to play a significant role in many chemical reactions, biological processes, and industrial technologies. Our comprehension of the effects of intermolecular association through Hbonding on diffusion in dense fluids is nonetheless relatively rudimentary at present. In particular, it appears that still very little information is available concerning the various internal effects of molecules (e.g., intramolecular H-bonding and steric hindrance) that may affect the overall diffusivities of solutes capable of intermolecular H-bonding with the solvent molecules in liquid solutions. A better understanding of these intra- and intermolecular effects, however, should be useful to the development of diffusion-dependent processes and technologies. Unlike the diffusion of nonassociated molecules, which can be fairly well described by the renowned Stokes−Einstein− Sutherland relation or in terms of the recently improved molecular-hydrodynamic model for pseudoplanar1,2 and spherical3 solute molecules, the transport properties of solutes capable of H-bonding with solvent molecules are generally conceded as much more complicated to depict and thus to predict. As intermolecular H-bonds are often forming and breaking in liquids, diffusivity of a nonionic solute that is Hbonded with solvent molecules at a given temperature is determined primarily by the average size and shape of the diffusive entity (i.e., the solute−solvent complex) in the solution, which should in turn be largely dependent on the © 2017 American Chemical Society

overall strength of the solute−solvent intermolecular interaction. Note that different polar groups in solute and solvent molecules can produce different H-bond strengths. For various solutes with similar monomeric size and shape in nonelectrolyte liquid systems, the diffusion rates of the associated solutes are normally slower than those of the nonassociated ones because diffusivity generally varies inversely with particle size. Evidence of comparatively lower diffusivities of solutes that are H-bonded with polar solvent molecules has in fact been demonstrated by previous experimental measurements.4−8 Currently, the influence of intermolecular H-bonding association on diffusivity continues to receive a lot of attention in the literature.9−13 In a given solvent, one would expect that the strength of external Hbonding between solute and solvent should also be affected to some extent by number of internal factors such as steric hindrance and intramolecular H-bonding, in addition to the nature and number of unalike functional groups constituting the solute molecule. To have a better understanding of the diffusion behavior of solutes that form the H-bonds with solvent, it is hence useful to separately account for the internal and external contributions of solutes to diffusivity. In our former investigations,14,15 we indeed found by comparing different polar aromatic solutes of similar size and shape that their diffusivities in polar solvents are influenced by the existence of steric hindrance14 and intramolecular H-bondReceived: July 14, 2017 Revised: October 18, 2017 Published: November 8, 2017 10882

DOI: 10.1021/acs.jpcb.7b06930 J. Phys. Chem. B 2017, 121, 10882−10892

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The Journal of Physical Chemistry B Chart 1. Structures of the Major Aromatic Isomers Considered in This Work

ing14,15 within a solute molecule. The results indicated that the values of diffusion coefficients are generally enhanced by such internal effects. Similar evidence of structural effects of solute molecules on diffusion has been observed by Tominaga et al.8 in their study of the diffusivities of cyclohexanediols, cyclohexanetriols, and cyclopentanediol in ethanol. In a recent work, Rodrigo et al.12 have also noticed that the diffusivities of γaminobutyric acid in aqueous solutions are affected by intramolecular H-bonding. Nonetheless, previous findings appear to lack further study that can provide a more quantitative understanding of the internal effects. In the present investigation, our focus is on examining the diffusion behavior of o- and m-isomers of the disubstituted benzenes in acetone, with particular interest in quantifying the different effects of H-bonding on diffusivity. Recently, Price et al.9 have applied the NMR method to measure the diffusivities of catechol, resorcinol, and hydroquinone (i.e., the o-, m-, and p-dihydroxybenzene, respectively) in water−alcohol mixtures. Although the diffusivities of these three isomers are nearly the same in aqueous solution, the investigators have found that the diffusivity of catechol is different from those of the other two isomers in water−monohydric alcohol systems.9 The emphasis of their study is on understanding the diffusion behavior of the three particular isomers in relation to different solution microstructures, which is useful for improving the technique of matrix-assisted diffusion-ordered spectroscopy for noninvasive analysis of liquid mixtures. In this work, our emphasis is on studying the diffusion behavior of different types of aromatic isomers in a given solvent. The objective is to obtain an insight into the roles that different polar groups play in affecting the effects of intra- as well as intermolecular Hbonding on diffusivity. The solute isomers in this work contain various functional groups on the benzene ring. The polar

groups include mainly hydroxyl and amine groups, which are commonly found in drugs and biological molecules. They are generally known to form strong H-bonds with polar solvents. Another important functional group in the present study is the nitro group, which is a strong electron-withdrawing group. The solutes are chosen to provide not only a study on the overall intermolecular effects but also a systematic investigation on the internal effects such as steric hindrance, properties of functional groups, and intramolecular H-bonding of the solutes on diffusivity. Pure acetone is used as the only solvent in our first study of this kind because, unlike water and alcohols, it does not form a complicated H-bonding network. It should be pointed out that in a solvent with H-bonding network, solute− solvent interactions may affect the relative strength of neighboring solvent−solvent H-bonds and consequently the overall size of a solute−solvent complex. Also, in this study, each acetone molecule can only utilize its oxygen atom to attach to a hydrogen atom in a polar functional group of a solute molecule to yield H-bonds. These characteristics of acetone facilitate simplicity for the straightforward identification and hence estimation of each of the different contributions to the effects of solute−solvent association on diffusion. Here, we present and analyze the measured diffusivities, together with the literature data, to unravel the relationship between the external and the internal effects of disubstituted benzene molecules on diffusion. It is also the purpose of this work to show a relation in terms of molecular volume and overall acidity of solutes that can accurately account for the diffusivities of aromatic amines and phenols in acetone.

2. EXPERIMENTAL SECTION The Taylor dispersion method was adopted in this work for measuring the limiting mutual diffusivities (mutual diffusion 10883

DOI: 10.1021/acs.jpcb.7b06930 J. Phys. Chem. B 2017, 121, 10882−10892

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The Journal of Physical Chemistry B Table 1. Diffusivities and Diffusivity Ratios of Disubstituted Benzenes in Acetone at 298.15 K

nonassociated solutes H-bonded solutes

a

diffusivity of o-isomer

diffusivity of m-isomer

diffusivity ratio

(Do12/10−9 m2 s−1)

−9 (Dm m2 s−1) 12/10

(Do12/Dm 12)

xylene dichlorobenzene toluidine cresol nitroaniline nitrophenol aminophenol dihydroxybenzene

3.39 3.35 3.03 2.78 2.77 3.06 2.63 2.50

± ± ± ± ± ± ± ±

a

0.04 0.03a 0.02 0.02b 0.03 0.04 0.03 0.02b

3.42 3.38 2.96 2.71 2.64 2.59 2.43 2.27

± ± ± ± ± ± ± ±

a

0.03 0.04a 0.03 0.03b 0.02 0.03 0.03 0.02b

0.99 0.99 1.02 1.03 1.05 1.18 1.08 1.10

From ref 24. bFrom ref 14.

coefficients at infinite dilution) of the disubstituted benzenes in acetone. This method has been widely used in recent diffusivity measurements11−13,16−19 due primarily to the fact that it allows not only precise but also fast acquisition of the diffusion data. Additional advantages of utilizing this method, known also as the chromatographic peak-broadening technique,18,20 have been given by Shevtsova et al.17 The experimental techniques involved in the method have been described by Grushka et al.,21 and the fundamental principles have been reviewed by Tyrrell and Harris22 and also by Cussler.23 The equipment, instruments, and procedures for the experimental measurement in this work were the same as those reported in our recent studies.1,2 In brief, a stainless-steel capillary tubing (1.59 mm o.d. and 0.762 mm i.d.) of length 91.4 m was employed as the diffusion tube. It was coiled into a circle with a radius of approximately 12 cm and immersed in a Julabo thermostat bath (model FP45) controlled to within ±0.01 K of a temperature. A small sample (approximately 20−50 μL) of a dilute solute solution was injected into a preheated stream of pure acetone flowing in the capillary diffusion tube. The flow rate of the solvent, which was slow between 0.1 and 0.16 mL min−1, was regulated within a precision of ±0.5% by an high-performance liquid chromatography pump (Agilent model 1100) to ensure a laminar flow. At the end of the tube, a Shimadzu differential refractometer (model RID-10A) was used to detect the eluted peak. In this study, all of the diffusivities were measured at 298.15 K, which was monitored with a certified thermometer (Baird and Tatlock, No. GDZ27736). All of the chemicals used in the present work were reagent grade. The solvent acetone (Aldrich, 99.9%+) was first degassed in a flask by using an ultrasonic bath. It was subsequently passed through a stainless-steel 20 μm solvent filter before transferring into the solvent delivery system for the experiment. The solutes m-nitroaniline, o-nitrophenol, mnitrophenol, o-aminophenol, and m-aminophenol were all E. Merck chemicals with 99%+ purity. These and other solutes onitroaniline (99%+), o-toluidine (99.5%+), and m-toluidine (99%+) of Fluka as well as hexamethylbenzene (99%+) of Aldrich were used as received. Note that each solute measurement was repeated at least four times to obtain an average diffusivity value for report here. The precision of the data was generally found to be approximately ±1%.

data is the precision of the measurement. Also shown in the table are the literature diffusivities of the o- and m-isomers of xylene (dimethylbenzene) and cresol (methylphenol), as well as those of catechol (o-dihydroxylbenzene) and resorcinol (mdihydroxylbenzene), which are useful for comparison and discussion later in this work. In Table 1, the symbols Do12 and m represent the diffusivities of the o- and m-isomers, D12 respectively. The ratios of the diffusivities (Do12/Dm 12) are also given in this table for all of the pairs of isomers studied. Except for the nonassociated xylenes and dichlorobenzenes, the isomers capable of H-bonding with acetone show Do12/Dm 12 values greater than 1, indicating that the H-bonded o-isomers diffuse faster than their m-isomer counterparts. The implication of the results for each pair of the H-bonded isomers in this investigation is that acetone is more strongly associated with the m- than with the o-isomer because stronger solute−solvent associations would normally lead to larger associated entities on the average in solution. Due to the size effect, the overall diffusion rates of the strongly associated solutes would be slower than those of the weakly associated ones. From the Do12/ Dm 12 ratios listed in Table 1, one would expect that the differences in diffusivity of the isomers are likely influenced by the extent of steric hindrance, intramolecular H-bonding, and electron-donating or -withdrawing effects that may occur within each of the solute molecules, in particular the o-isomers. Such influences as well as the effects of molecular shape on diffusion of the disubstituted benzenes in acetone are individually evaluated and discussed below. Structural isomers such as those displayed in Chart 1 are generally different in molecular shape. Table 1 shows the literature diffusivities of the o- and m-isomers of xylene as well as dichlorobenzene in acetone at 298.2 K. Except for the small differences in shape, each pair of these isomers are equal in molecular volume and mass, and all of the compounds are unable to form H-bonds with acetone. For nonassociated solute molecules of van der Waals (VDW) volume between approximately 80 and 180 × 10−3 nm3, the diffusivities in acetone at 298.15 K were previously found to be fairly insensitive to the different shapes and masses of the solute molecules.25 As also shown in Table 1, the diffusivity ratios o m /D 12 ) for the o- and m-isomers of xylene and (D 12 dichlorobenzene are both 0.99, indicating that the effects of solute shape on diffusivity for the nonassociated solute isomers are indeed fairly insignificant within the experimental precision of about ±1%. For a pair of o- and m-isomers that are capable of forming H-bonds with acetone, however, the average sizes of their solute−solvent complexes may not be the same due to possible difference in the degree of association. Hence, their relative shape effect on diffusivity could be slightly different

3. RESULTS AND DISCUSSION The molecular structures of the aromatic solutes of primary concern in this investigation are shown in Chart 1. The limiting mutual diffusivity (D12) data as measured by the Taylor dispersion method for the disubstituted benzenes are presented in Table 1. The ± value listed after each of the D12 10884

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The Journal of Physical Chemistry B

functional groups −CH3, −OH, and −NH2 are actually isoelectronic in structure and thus fairly similar in size. One of the major objectives of the present work is to unveil the effects due to intramolecular H-bonding on diffusion. For the disubstituted benzenes considered in this study, the combined effects of steric hindrance and solute shape on diffusivity are small, with an average difference in diffusivity of about +2.5% greater for o- than for m-isomers in acetone as the solvent. Note that a nitro group is not much larger than a methyl group, and both cannot form H-bonds with acetone. Thus, if the Do12/Dm 12 ratios of nitroaniline and nitrophenol represent the combined effects of steric hindrance and solute shape on diffusivity between their o- and m-isomers, the values of the ratios are then expected to be similar to those of toluidine and cresol, respectively. Nonetheless, Table 1 shows that the Do12/Dm 12 ratios for the isomers of nitroaniline and nitrophenol are 1.05 and 1.18, respectively. It should be pointed out that a proton in −NH2 of o-nitroaniline or in −OH of onitrophenol can form an intramolecular H-bonding with an oxygen atom in −NO2 of the o-isomers, whereas no such bonding can occur in the o-isomers of toluidine and cresol. Intramolecular H-bonding is also not possible in the m-isomers of nitroaniline and nitrophenol, however, because the protondonating and proton-accepting groups are further apart. By considering the results for toluidine and cresol, the combined effects of solute shape and steric hindrance on diffusivity that can render faster diffusion rates for the o-isomers than for the m-isomers can be similarly estimated as 2% for o-nitroaniline and 3% for o-nitrophenol. From the Do12/Dm 12 ratios given in Table 1, the effects due to intramolecular H-bonding on diffusivity can then be reasonably evaluated to be +3 and +15% for the o-isomers relative to their m-counterparts of nitroaniline and nitrophenol, respectively. The effects obtained for these two o-isomers are thus quite different. Note that both oisomers can form a stable six-member ring through an intramolecular H-bonding.10 One possible explanation for the pronounced difference in the intramolecular H-bonding effects (H-B eff) is again because there are two protons in −NH2, whereas there is only one in −OH. Although a proton in −NH2 forms an intramolecular H-bond with −NO2 in o-nitroaniline, another is still available for an intermolecular H-bonding with acetone. Nonetheless, this is not the case for o-nitrophenol, which has only one proton for intramolecular H-bonding. Similar explanation can be given for aminophenol and dihydroxybenzene, where not all of the protons in their oisomers are involved in forming intramolecular H-bonds. Table 1 indeed shows that the Do12/Dm 12 ratios of these compounds are lower than that of the nitrophenol. Note that both the −NH2 and the −OH groups are slightly smaller than a methyl group, and thus the combined effects of solute shape and steric hindrance on diffusivity can be reasonably approximated to be +2% for both o-aminophenol and o-dihydroxybenzene. Hence, the effects of intramolecular H-bonding on diffusivity can be evaluated, after a 2% correction, as 6 and 8% between the oand m-isomers of aminophenol and dihydroxybenzene, respectively. In the above analysis, we have shown that intramolecular Hbonding in the o-isomers of aromatic solutes could reduce the solute−solvent interactions, rendering the diffusivities of the oisomers greater as compared to those of their m-counterparts. For the disubstituted aromatic isomers studied, the effects of intramolecular H-bonding on diffusivity are found to range from 3 to 15%, depending on the nature of the substituents on

from that of a pair of nonassociated o- and m-isomers with similar monomeric size. Nonetheless, the solute−solvent complexes are not expected to deviate very much from the pseudoplanar structure. The reason is that acetone molecules can only associate with proton-donating groups on the side of a benzene ring of the aromatic solutes, which is basically planar in structure. Also, acetone is a relatively small molecule. In the extreme case between spherical and pseudoplanar solutes, the effects of shape on diffusivity have recently been shown to range from 0% for molecular volume around 120 × 10−3 nm3 to only about 6% for the size of approximately 210 × 10−3 nm3, with the spherical solutes having greater diffusivity.26 Thus, we believe that the uncertainty of the effects due to the “relative” differences in shape (not size) on diffusivity between the isomeric complexes and their monomers can be reasonably estimated to be less than +2% for the complexes in the present investigation. Steric effects plays an important role in many molecular processes, especially those in connection with H-bonded complexes.27,28 For the disubstituted benzenes studied in this work, all of the o-isomers have an adjacent functional group, but m-isomers do not. It is of interest to compare the Do12/Dm 12 ratios of the toluidine and cresol isomers. Both of these solutes have a nonpolar methyl group and a polar group (see Chart 1) that can form a relatively strong H-bond with acetone. Nonetheless, a methyl group in the o-isomers can likely hinder the approach of any acetone molecule to form an H-bond with either the −NH2 or −OH group in the adjacent ortho position, whereas no such steric hindrance could happen to the misomers without an adjacent group. Consequently, the extent of H-bonding and thus the average size of complex formed should be less for o-isomer as compared to those of m-isomer in the present study. As it can be seen in Table 1, the Do12/Dm 12 values for toluidine and cresol are 1.02 and 1.03, respectively. These ratios suggest not only that o-isomer diffuses slightly faster than m-isomer in both cases, but also that the values represent the combined effects of solute shape and steric hindrance on diffusivity for the two pairs of isomers. From the Do12/Dm 12 values, one can deduce the effect due solely to steric hindrance by subtracting the ratio for each pair of isomers by the effect of solute shape on diffusivity. Based on the results in the previous paragraph, the effects of solute shape contribute −1% to the Do12/Dm 12 ratios, and thus the effects of steric hindrance on diffusivity that cause the o-isomers of toluidine and cresol to have greater diffusivity values than their m-counterparts can be estimated to be about 3 and 4%, respectively. The small steric effect observed for o-toluidine is not unexpected because −NH2 has two hydrogen atoms that can form H-bonds. When one is hindered by the methyl group, another one can still form an intermolecular H-bond with acetone. Although all of the cresol isomers have only one −OH group, the similarly small effect found for o-cresol as for o-toluidine is probably because the hydrogen atom in the −OH group is turned away from the methyl group, rendering it still capable of H-bonding with acetone to some extent. This structural arrangement of o-cresol has been concluded by the conformation energy study of Allinger et al.29 It should be noted that all of the functional groups considered in this study are generally small and not very much different in size as compared to a methyl group, whose volume is 21.4 × 10−3 nm3.2 The size (in 10−3 nm3) of −NO2 that cannot associate with acetone is relatively greater at 27.9, and those of −OH and −NH2 that are capable of forming Hbonds with the solvent are 13.4 and 17.6, respectively.2,15 The 10885

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The Journal of Physical Chemistry B Table 2. Experimental and Calculated DN12 for Nonassociated Pseudoplanar Solutes in Acetone at 298.15 K solutes benzene toluene ethylbenzene o-xylene m-xylene naphthalene 1,2,4-trimethylbenzene mesitylene biphenyl hexamethylbenzene a

V1/10−3 nm3 81.1 97.6 113.8 114.2 114.2 125.4 130.7 130.7 152.4 180.3

DN12/10−9 m2 s−1 4.16 3.75 3.45 3.39 3.42 3.25 3.16 3.16 2.89 2.65

b

± ± ± ± ± ± ± ± ±

0.03 0.02 0.04 0.03 0.03 0.04 0.03 0.03 0.04

refs

calc DN12/10−9 m2 s−1a

25, 27, 28 25 25 24 24 25 14 29 25 this work

4.08 3.74 3.45 3.44 3.44 3.27 3.19 3.19 2.91 2.62

Calculated by eq 1. bAverage value from refs 25, 30, 31.

the benzene ring of the aromatic compounds. The results indicate that these intramolecular effects are quite significant. Table 2 shows the limiting mutual diffusivities of 10 pseudoplanar hydrocarbons in acetone at 298.15 K, which were obtained from various sources including this work. The solutes chosen are basically nonpolar aromatic compounds that cannot form H-bonded association with the solvent molecules. Also listed in the table are the VDW volumes (V1) of the solutes. These V1 values, ranging approximately from 81 to 180 × 10−3 nm3, were calculated from group increments given in ref 2. For nonassociated solutes of similar shape diffusing in a given solvent at constant temperature, it is known that there exists a linear relationship between the reciprocal of diffusivity and V1 of the solutes, provided that the range of the solute sizes is not extraordinarly wide.1,7,25,26 In this work, the data in Table 2 can indeed be represented very well by the following equation N −1 (D12 ) /108 m−2 s = 1.38 × 10−2V1/10−3 nm 3 + 1.33

(1)

DN12

where is the diffusivity of a nonassociated pseudoplanar solute. Equation 1 fits all of the reciprocals of the diffusivities in Table 2 to within ±1.9%, whereas the % standard deviation between the experimental and calculated DN12 values is only 0.56%. The correlation coefficient for the linear regression is 0.997. A plot of (DN12)−1 versus V1 is displayed in Figure 1 as well as in Figure 2. Table 2 also gives the DN12 values calculated by eq 1 for the nonassociated solutes. As shown in this table, the agreements between the experimental and calculated diffusivities are very good. The reciprocals of the diffusivity data in Table 1 for the isomers of the aromatic amines are plotted in Figure 1, whereas those of the phenolic compounds (phenols) are plotted in Figure 2. It is clear from these figures that all of the (D12)−1 values of the polar solutes capable of H-bonding with acetone deviate positively from the straight line of the nonassociated solutes, with the m-isomers consistently higher than their ocounterparts. By utilizing the linear regression line, one can compare the (D12)−1 value of any proton-donating (Hdonating) solute with the (DN12)−1 value of a nonpolar solute, both of the same VDW volume V1. Table 3 shows the calculated (DN12)−1 values of the H-donating solutes considered in this work. These values are calculated by eq 1 using the monomeric V1 of the solutes, i.e., they represent the diffusivities of the solutes as if they behave like nonassociated solutes in acetone at 298.2 K. Given also in Table 3 are the (D12)−1/calc (DN12)−1 ratios for the solutes, which are equivalent to calc (DN12)/D12 ratios and are all greater than 1. The ratios, ranging

Figure 1. Plot of (D12)−1 vs V1 for aromatic amines in acetone at 298.2 K: o-toluidine ▲, m-toluidine Δ, o-aminophenol ●, m-aminophenol ○, o-nitroaniline ■, and m-nitroaniline □. The straight line represents linear regression for nonassociated solutes ×.

from 1.14 to 1.65 in this study, indicate that the nonpolar solutes diffuse faster than the H-donating ones of same molecular size by 14 to 65%. This implies that the diffusion rates of the H-donating solutes are retarded by the formation of H-bonded solute−solvent associations. Note that acetone is a dipolar molecule, and that the lower diffusivities of the polar solutes cannot be due to solute−solute associations because the solutes are very dilute in a relatively polar solvent. It should also be pointed out that evidence has been given that aniline is not even self-associated in a nonpolar n-tetradecane solvent.7 All of the ratios for the o-isomers in Table 3 appear to be smaller than those of their m- and p-counterparts, suggesting that they diffuse comparatively faster than the other isomers. As discussed earlier in this section, the faster diffusion rates of the o-isomers rather than the m- or p-isomers can be attributed to a combination of the effects of intramolecular H-bonding, shape, and steric hindrance in the o-isomers that could reduce the extent of solute−solvent intermolecular interactions. 10886

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of 0.87 above, indicating that the extents of intermolecular association are probably reduced by steric hindrance due to the presence of an adjacent methyl group in the molecules. Interestingly, the value for 2,6-dimethylphenol is much lower, obviously because there are two adjacent methyl groups in that molecule that can hinder the approach of acetone molecules to form a H-bond with the −OH group. Similar results are observed for the aromatic amines with only one polar amino group. The mean value for aniline, p-toluidine, and m-toluidine is 0.54. The value for o-toluidine, however, is 0.45. Likewise, the lower value is also attributable to steric hindrance in the oisomer. It is interesting to compare the ΔD12−1/108 m−2 s values of the disubstituted benzenes with two polar groups. The values for p- and m-dihydroxybenzene containing two −OH groups are 1.74 and 1.73, respectively. These values are about the same and nearly twice the mean value of 0.87 for compounds containing a single −OH group without steric hindrance. The results thus appear to suggest that the ΔD12−1 values are additive, depending on the number of −OH groups in the solute molecule. This is true for p- and m-dihydroxybenzene without the steric hindrance; however, the value for odihydroxybenzene is 1.32, which is clearly smaller due to steric hindrance and intramolecular H-bonding. In the case of the nitrophenols, the m-isomer is 0.98, whereas the o-isomer has a very low value of 0.39. Both isomers have only one −OH group for H-bonding with acetone. Although the difference between their ΔD12−1 values can be understood in terms of intramolecular H-bonding and steric hindrance, the magnitudes of their values seem to require further explanation. Table 3 clearly shows that the value of the m-isomer is not quite the same as those of phenol, p-cresol, and m-cresol, although all have a single −OH group that is free from steric hindrance and intramolecular H-bonding in their molecule. However, mnitrophenol has in addition a polar nitro group, which is a strong electron-withdrawing functional group that withdraws electron density from the benzene ring.37 Note that −OH as a whole is an electron-donating group that donates electron density to the benzene ring.37 When these two different groups coexist in an aromatic compound, they tend to reinforce each other’s electronic properties by making the −OH group more acidic and the nitro group more basic. Hence, the −OH group can form a stronger H-bonded association with acetone, even though the nitro group cannot. It is therefore not surprising to observe that the value of ΔD12−1 is greater for m-nitrophenol than for other phenols with a single −OH group but without intramolecular H-bonding and steric hindrance. Similar situation is found for m- and o-nitroaniline, as the amino group as a whole in the isomers is electron-donating to the benzene ring.37 As shown in Table 3, the ΔD12−1 value of mnitroaniline (0.85) is indeed greater than those of aniline (0.53), p-toludine (0.55), and m-toludine (0.53) with only one amino group. On the other hand, the smaller value of onitroaniline (0.67) as compared to that of m-nitroaniline is again attributable to steric hindrance and intramolecular Hbonding in the o-isomer. Moreover, the case for the aminophenols resembles that of the dihydroxybenzenes. For similar reason given above, the value of o-aminophenol (1.06) is lower than that of m-aminophenol (1.38). It also appears that the value of the m-isomer is the sum of two contributions, one from the amino group (mean = 0.54) and another from the −OH group (mean = 0.87). Note that both −NH2 and −OH are electron-donating groups. Their coexistence on a benzene

Figure 2. Plot of (D12)−1 vs V1 for phenolic compounds in acetone at 298.2 K: o-cresol ⧫, m-cresol ◊, o-aminophenol ●, m-aminophenol ○, o-nitrophenol (circle containing a small filled circle), m-nitrophenol ◎, o-dihydroxybenzene ⊞, and m-dihydroxybenzene (square containing a small filled square). The straight line represents linear regression for nonassociated solutes ×.

In addition to the ratios discussed above, the values of ΔD12−1 are also provided in Table 3 for consideration. Each of these values actually represents the deviation of a solute’s D12−1 value from the nonassociated line, i.e., D12−1 − calc (DN12)−1. The magnitude of ΔD12−1 has already been shown to be related to the increase in the size of a solute (from a monomer to an associated complex) that causes the lowering of its diffusivity.15,35 It has also been found to vary linearly with the calculated solute−solvent interaction energies.35 Hence, it is of interest to examine the values of the H-donating solutes studied, in particular those of the isomers that can provide useful information concerning their relative effects of intermolecular H-bonding on diffusivity. Considering the precision (±1%) of the experimental diffusivities and the standard deviation (±0.56%) of calc (DN12)−1, one can estimate that the uncertainties for the ΔD12−1 values. Table 3 also lists the uncertainty for each of these values. It should be pointed out, however, that the “relative” uncertainties between the values of the isomers should be less because same value of calc (DN12)−1 is used for calculating the ΔD12−1 values of the isomers. By comparing the phenolic compounds containing only one polar −OH group, Table 3 shows that the values of ΔD12−1/108 m−2 s for phenol, p-cresol, and m-cresol are approximately the same, with the mean being 0.87. The results are not surprising, as similar findings in other studies have been reported.35,36 It is reasonable to expect that a same H-donating group in different aromatic compounds would provide same intermolecular interactions with molecules of a given solvent, unless the Hdonating group is affected by steric hindrance or by other Haccepting groups in the compound. Indeed, the values given in the table for o-cresol and 2,5-dimethylphenol (also with only one polar −OH group) are slightly smaller than the mean value 10887

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110.4 102.3 102.3 116.8 116.8

o-toluidine m-aminophenol o-aminophenol m-nitroaniline o-nitroaniline

10888

S, I E S, I, E

S

S, I E S, I, E

S S S

intramolecular activitiesc

2.62 2.85 2.85

3.15i 3.40i 3.38 2.85 2.74 2.74 2.94 2.94

2.80 3.02 3.02 2.68 2.68 2.68 2.88 2.88

3.60j 3.83j 3.64j 4.42j 4.41j 4.00j 3.86 3.27

3.30 4.12 3.80 3.79 3.61

2.57 2.80 2.80

calc (DN12)−1/108 m−2 se

3.41i 3.68i 3.69j

(D12)−1/108 m−2 sd

1.16 1.50 1.39 1.29 1.23

1.20 1.19 1.19

1.29 1.27 1.21 1.65 1.65 1.49 1.34 1.14

1.33 1.31 1.32

(D12)−1/calc (DN12)−1

0.53 ± 0.05 0.55 ± 0.05 0.53 ± 0.05 mean = 0.54 0.45 ± 0.05 1.38 ± 0.06 1.06 ± 0.05 0.85 ± 0.05 0.67 ± 0.05

0.84 ± 0.05 0.88 ± 0.05 0.89 ± 0.05 mean = 0.87 0.80 ± 0.05 0.81 ± 0.06 0.62 ± 0.05 1.74 ± 0.06 1.73 ± 0.06 1.32 ± 0.06 0.98 ± 0.06 0.39 ± 0.05

ΔD12−1/108 m−2 sf

0.37 1.04 0.96 0.64 0.48

0.42 0.37 0.37

0.83 0.86 0.62 1.86 1.76 1.36 1.26 0.08

0.96 0.91 0.91

calc ΔD12−1/108 m−2 sg

13.6 33.5 27.9 22.4 18.6

16.8 16.2 15.7

22.2 21.1 17.0 39.4 39.2 33.0 25.4 11.9

24.6 23.9 24.1

% H-B effh

Calculated from group increments given in refs 2 and 3, except nitro group from ref 32. bFrom refs 33 and 34. cS (steric hindrance), I (intramolecular H-bonding), and E (interaction between electronwithdrawing and -donating groups). dThis work, except where noted otherwise. eCalculated by eq 1 using solute molecules V1. fΔD12−1 = (D12)−1 − calc (DN12)−1. gCalculated by eq 4 using c = 1.60. h [(Calc DN12 − D12)/calc DN12] × 100%. iFrom ref 35. jFrom ref 14.

a

0.26 0.23 0.23

93.8 110.4 110.4 0.23 0.65 0.60 0.40 0.30

0.52 0.54 0.39 1.16 1.10 0.85 0.79 0.05

0.60 0.57 0.57

∑αHb

106.2 122.7 122.7 98.1 98.1 98.1 112.6 112.6

89.6 106.2 106.2

V1/10−3 nm3a

o-cresol 2,5-dimethylphenol 2,6-dimethylphenol p-dihydroxybenzene m-dihydroxybenzene o-dihydroxybenzene m-nitrophenol o-nitrophenol aromatic amines aniline p-toluidine m-toluidine

phenolic compounds phenol p-cresol m-cresol

solute

Table 3. Values of V1, ∑αH, D12−1, Calc (DN12)−1, ΔD12−1, Calc ΔD12−1, and % H-B Eff of Solutes in Acetone at 298.15 K

The Journal of Physical Chemistry B Article

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Article

The Journal of Physical Chemistry B ring cannot increase the overall acidity of an aromatic compound to form a stronger H-bond with acetone. Hence, it is not unexpected to find similar additive nature of the ΔD12−1 value in m-aminophenol as in m- and p-dihydroxybenzene. It should be noted that diffusivities of the p-isomers of nitrophenol, aminophenol, and nitroaniline were not measured in this work, as it is quite clear from the results of the m- and p-isomers of cresol, dihydroxybenzene, and toluidine (see Table 3) that they should be approximately the same as those of the m-isomers. One interesting feature in the values of ΔD12−1 is noteworthy. All of the four o-isomers containing two polar groups in Table 3 are capable of intramolecular H-bonding, and their ΔD12−1 values are nonetheless not zero, i.e., they do not behave as nonassociated solutes. The result is understandable for the o-isomers of dihydroxybenzene, aminophenol, and nitroaniline. Although an o-isomer of these solutes forms an intramolecular H-bond between two polar groups with Haccepting and -donating atoms, there is still at least one proton free in the groups for intermolecular H-bonding with acetone. However, o-nitrophenol does not have any more proton available after intramolecular H-bonding. The nonzero ΔD12−1 value of this isomer apparently suggests that there is probably still small amount of H-bonding between acetone and the isomer. One possible explanation is that the intramolecular Hbond in the molecule is perhaps not completely frozen, i.e., the −OH group may still have some degree of restricted rotation that it can loosely form an intermolecular H-bond with acetone. Nonetheless, this interpretation would await further investigation to verify. Table 3 also lists the values of % H-B eff (% hydrogenbonding effect) for the H-donating or electron-accepting polar solutes. These values, varying from 11.9 to 39.4%, are calculated by the following expression N N % H‐B eff = [(calc D12 − D12)/calc D12 ] × 100%

Figure 3. Percent effects of intermolecular H-bonding on diffusivities of polar disubstituted benzenes in acetone at 298.2 K; solid bars represent m-isomers without intramolecular H-bonding, hollow bars refer to o-isomers with intramolecular H-bonding, and short straight lines denote estimated uncertainties of the bars.

respectively. Because the strength of H-bond determines the fraction of time the molecule is bonded to the solvent and thus the average size of the diffusing H-bonded complex, it follows that ΔD12−1 can also be expressed by ΔD12−1 ∝

∑ αH ∑ βH

(3)

The ∑α values for the solutes studied, which have been collected from the literature,33,34 are listed in Table 3. The ∑βH value for acetone is 0.49.33,34 Note that the experimental errors reported for the ∑αH and ∑βH values are about 0.03 units.34 For solutes diffusing in a given solvent at constant temperature, ∑βH for the solvent can be considered as a constant, and eq 3 can then be written as follows H

(2)

where D12 is the experimental diffusivity of the H-donating solute and calc DN12 denotes the diffusivity value calculated by eq 1 (for nonassociated solutes) using the H-donating solute’s V1 value. Each value of % H-B eff in Table 3 thus represents the % effect of intermolecular H-bonding on diffusivity for a solute in acetone at 298.15 K. Quantitative comparisons of such % effects between o- and m-isomers are shown in Figure 3. As expected, all of the values of % H-B eff are lower for the oisomers than for the m-isomers. It is of interest to compare the relative values for the o- and m-isomers of nitroaniline and nitrophenol in Figure 3. For reason given above with respect to the number of hydrogen atoms available for H-bonding, the reduction in the % H-B effect of the o-isomers can be observed to be relatively much greater for nitrophenol than for nitroaniline. Two H-bond scales, ∑αH and ∑βH, for representing the effective acidity and basicity, respectively, of chemical compounds have been established by Abraham.33,34 The values of these overall H-bond acidity and basicity of molecules were primarily derived from the complexation constants of two solutes in different solvents. They can actually be viewed as the relative ability of a compound to donate or accept a proton for forming a H-bonded complex with another compound. If a solute can donate a proton to form a H-bond with acetone, it is reasonable that their H-bonding strength should be proportional to the product ∑αH∑βH, where ∑αH and ∑βH are the effective acidity and basicity of the solute and acetone,

ΔD12−1 = c ∑ α H

(4)

where c is a proportional constant. In fact, we have previously shown that ΔD12−1 can correlate fairly well with ∑αH for monofunctional type of aromatic solutes in acetone at 298.2 K.38 It is of interest to know if eq 4 is applicable also to aromatic compounds containing two polar functional groups. The values of ΔD12−1 in Table 3 were thus fitted against the ∑αH values of the solutes. With c = 1.60 ± 0.06, we have found that eq 4 is fairly satisfactory in correlating the data. A plot of ΔD12−1 versus ∑αH is shown in Figure 4. The calculated values of ΔD12−1 are shown also in Table 3 for comparison with the experimental values. It is noteworthy that Abraham has pointed out that the ∑βH values of aromatic amines and pyridines are slightly solvent dependent.33 Whether it is also true for the values of ∑αH is not known. Nonetheless, as shown in Table 3, the agreements between the calculated and the experimental values are generally not as good for the aromatic amines as for the phenols (except o-nitrophenol with a very low ∑αH value of 0.05). In consideration of the overall precision (approximately ±1%) of the diffusivity data and the uncertainty (∼0.03 units) in the ∑αH values, however, the linear dependence of ΔD12−1 on ∑αH with only one parameter c is quite acceptable. From the definition of ΔD12−1 given in Table 3, (D12)−1 can be expressed by 10889

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The Journal of Physical Chemistry B

the % standard deviation between the calculated and the experimental values is 2.8%.

Figure 4. Variation of ΔD12−1 with ∑αH. N −1 D12−1 = calc(D12 ) + ΔD12−1

(5)

By substituting eq 4 into eq 5, one can obtain the following relation N −1 D12−1 = calc(D12 ) + c ∑ αH

Figure 5. Plot of calculated D12 vs experimental D12.

(6)

4. CONCLUSIONS Diffusion rates of solute molecules capable of solute−solvent association through H-bonding are often of critical importance to many chemical, biological, and industrial processes. Nonetheless, the diffusion behavior of H-bonded solutes, in particular those diffusivities that are affected by intramolecular activities, is still not quantitatively well understood. In this study, we demonstrate that carefully designed measurements of the diffusivities of polar H-donating (electron-accepting) aromatic solutes in acetone can be used to probe intermolecular as well as intramolecular effects of solute molecules on diffusivity. Comparisons between the measured diffusivities of the oand m-isomers of different disubstituted benzenes reveal that their diffusivities are not very sensitive to the differences in shape of the isomers. Nonetheless, it is evident from the data of the isomers containing a single polar H-donating group for forming H-bonds with the H-accepting acetone that there is indeed a small effect of steric hindrance in every o-isomer. Steric hindrance acts to weaken the solute−solvent association and consequently enhances the diffusivity of a solute molecule. For all of the o-isomers containing two polar groups that can form intramolecular H-bonds, the diffusivities are found to be even relatively greater than those of the m-counterparts, indicating that, in addition to steric hindrance, the intermolecular associations are further weakened by the intramolecular H-bonding. With small corrections for the effects of shape and steric hindrance on diffusivity, we further demonstrated that the effects due to intramolecular H-bonding can be quantitatively evaluated. These effects are found to vary from +3 to +15% for the o-isomers as compared to their m-counterparts in this investigation, which are quite significant. By comparing the diffusivity reciprocals of the associated solutes with those of the nonassociated aromatic compounds of

Using eq 1 for representing calc (DN12)−1 and 1.60 for the value of c, eq 6 can be rewritten for predicting the diffusivities of solutes in acetone at 298.2 K as D12−1 = (1.38 × 10−2V1/10−3 nm 3 + 1.33) + 1.60

∑ αH (7)

We have applied eq 7 to calculate the diffusivities (D12) of the 19 polar solutes in Table 3, and the calculated values agree with the experimental ones fairly well within a % standard deviation of only 2.95%. The maximum absolute error is 10.5%, which is due to o-nitrophenol. The large deviation of this compound is not unexpected because both its ∑αH and ΔD12−1 values are very small with relatively large experimental errors. As discussed in the previous paragraph, the fitting by eq 4 for this isomer is less satisfactory. Thus, the expression 1.60 ∑αH obtained as a result of eq 4 should be less accurate for representing onitrophenol in the calculation of D12−1 or D12 by using eq 7. Generally, the prediction of the diffusivities of the H-bonded solutes by eq 7 is quite good, in particular that there are large differences between the diffusivities of the associated and the nonassociated solutes of same monomeric size. It is noteworthy that the diffusivities could be overestimated by 14−65% if the correction for association is not made. Equation 7 is actually a general equation that can be used for predicting the diffusivities of nonassociated as well as H-bonded solutes in acetone at 298.2 K. For nonpolar solutes that are unable to form H-bonds, the ∑αH value is zero. We have indeed applied eq 7 to calculate the diffusivities for all of the 10 nonpolar solutes in Table 2 and the 19 associated solutes in Table 3. The calculated D12 values agree well with those of the experimental diffusivities. A plot of the calculated versus the experimental diffusivities is shown in Figure 5. For a total of 29 nonassociated and associated solutes listed in Tables 2 and 3, 10890

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Mixtures at the Infinite Dilution Limit. J. Chem. Phys. 1991, 94, 3867− 3871. (7) Chan, M. L.; Chan, T. C. Diffusion of Pseudoplanar Solutes: An Investigation on the Effects of Hydrogen Bonding. J. Phys. Chem. 1995, 99, 5765−5768. (8) Tominaga, T.; Tenma, S.; Watanabe, H. Diffusion of Cyclohexane and Cyclopentane Derivatives in Some Polar and Non-polar Solvents. Effect of Intermolecular and Intramolecular HydrogenBonding Interactions. J. Chem. Soc., Faraday Trans. 1996, 92, 1863− 1867. (9) Codling, D. J.; Zheng, G.; Stait-Gardner, T.; Yang, S.; Nilsson, M.; Price, W. S. Diffusion Studies of Dihydroxybenzene Isomers in Water−Alcohol Systems. J. Phys. Chem. B 2013, 117, 2734−2741. (10) Su, J. T.; Duncan, P. B.; Momaya, A.; Jutila, A.; Needham, D. The Effect of Hydrogen Bonding on the Diffusion of Water in nAlkanes and n-Alcohols Measured with a Novel Single Microdroplet Method. J. Chem. Phys. 2010, 132, No. 044506. (11) Plugatyr, A.; Svishchev, I. M. Molecular Diffusivity of Phenol in Sub- and Supercritical Water: Application of the Split-Flow Taylor Dispersion Technique. J. Phys. Chem. B 2011, 115, 2555−2562. (12) Rodrigo, M. M.; Esteso, M. A.; Barros, M. F.; Verissimo, L. M. P.; Romero, C. M.; Suarez, A. F.; Ramos, M. L.; Valente, A. J. M.; Burrows, H. D.; Ribeiro, A. C. F. The Structure and Diffusion Behaviour of the Neurotransmitter γ-Aminobutyric Acid (GABA) in Neutral Aqueous Solutions. J. Chem. Thermodyn. 2017, 104, 110−117. (13) Legros, J. C.; Gaponenko, Y.; Mialdun, A.; Triller, T.; Hammon, A.; Bauer, C.; Köhler, W.; Shevtsova, V. Investigation of Fickian Diffusion in the Ternary Mixtures of Water−Ethanol−Triethylene Glycol and Its Binary Pairs. Phys. Chem. Chem. Phys. 2015, 17, 27713− 27725. (14) Chen, S.; Xu, J.; Chan, T. C. Steric Effects on Diffusion of Associated Molecules in Acetone. Chem. Commun. 2002, 898−899. (15) Chan, T. C.; Chen, N.; Lu, J. G. Diffusion of Disubstituted Aromatic Compounds in Ethanol. J. Phys. Chem. A 1998, 102, 9087− 9090. (16) Ghanavati, M.; Hassanzadeh, H.; Abedi, J. Application of Taylor Dispersion Technique to Measure Mutual Diffusion Coefficient in Hexane + Bitumen System. AIChE J. 2014, 60, 2670−2682. (17) Mialdun, A.; Sechenyh, V.; Legros, J. C.; de Zárate, J. M. O.; Shevtsova, V. Investigation of Fickian Diffusion in the Ternary Mixture of 1,2,3,4-tetrahydronaphthalene, Isobutylbenzene and Dodecane. J. Chem. Phys. 2013, 139, No. 104903. (18) Srinivas, K.; King, J. W.; Howard, L. R.; Monrad, J. K. Binary Diffusion Coefficients of Phenolic Compounds in Subcritical Water Using a Chromatographic Peak Broadening Technique. Fluid Phase Equilib. 2011, 301, 234−243. (19) Rodrigo, M. M.; Valente, A. J. M.; Barros, M. C. F.; Verissimo, L. M. P.; Ramos, M. L.; Justino, L. L. G.; Burrows, H. D.; Ribeiro, A. C. F.; Esteso, M. A. Binary Diffusion Coefficients of L-histidine Methyl Ester Dihydrochloride in Aqueous Solutions. J. Chem. Thermodyn. 2015, 89, 240−244. (20) Dymond, J. H. Limiting Diffusion in Binary Nonelectrolyte Mixtures. J. Phys. Chem. 1981, 85, 3291−3294. (21) Grushka, E.; Kikta, E. J., Jr. Diffusion in Liquids. II. The Dependence of the Diffusion Coefficients on Molecular Weight and on Temperature. J. Am. Chem. Soc. 1976, 98, 643−648. (22) Tyrrell, H. J. V.; Harris, K. R. Diffusion in Liquids; Butterworths: London, 1984. (23) Cussler, E. L. Diffusion, Mass Transfer in Fluid Systems, 3rd ed.; Cambridge University Press: Cambridge, 2009. (24) Chan, T. C. Diffusion of Aromatic Compounds: An Investigation on the Effects of Molecular Shape, Mass, and Dipole Moment. J. Chem. Phys. 1984, 80, 5862−5864. (25) Chan, T. C.; Chan, M. L. Diffusion of Pseudo-planar Molecules: An Experimental Evaluation of the Molecular Effects on Diffusion. J. Chem. Soc., Faraday Trans. 1992, 88, 2371−2374. (26) Chan, T. C.; Li, H. T.; Li, K. Y. Effects of Shapes of Solute Molecules on Diffusion: A Study of Dependences on Solute Size, Solvent, and Temperature. J. Phys. Chem. B 2015, 119, 15718−15728.

same monomeric size, we are able to quantify the effects of intermolecular H-bonding on diffusivity. These effects, as expressed by % H-B eff in this work, are found to range from 11.9 to 39.4%, which can be attributed largely to the different extents of association between the solute and the solvent molecules. For solutes with two polar groups, the results clearly indicate that the effects due to intermolecular H-bonding are dependent not only on the nature of the functional groups but also on the existence of the intramolecular effects such as steric hindrance and intramolecular H-bonding in the molecules. An interesting finding in this work is that the electron-donating and -withdrawing properties of functional groups appear to play an important role in determining the degree of intermolecular association through H-bonding. It is also remarkable to observe the result that although intramolecular H-bonding occurs in the o-isomers, it does not completely prohibit the formation of weaker intermolecular association, even for o-nitrophenol with only one proton that can form the H-bond. Moreover, a general equation that can fairly well represent the diffusivities of the solutes investigated, including all of those that can and cannot associate with acetone through H-bonding, is developed in the present work. The notion is that diffusivity can be semiempirically interpreted as a combination of two contributions: one from nonassociation and another due to the extent of H-bonded association. In terms of VDW volume and overall acidity of solutes, eq 7 in this study is shown to be capable of predicting a total of 29 diffusivities of both the associated and the nonassociated solutes very well. The % standard deviation between the calculated and the experimental diffusivity values is 2.8%.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

T. C. Chan: 0000-0003-1619-9328 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We are grateful to the Research Committee of the Hong Kong Polytechnic University for support of this work under Grant No. 5-ZJF1. We also wish to express our thanks to H.T. Li, J.H. Xu, and K.Y. Li for their technical assistance.

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REFERENCES

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