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London Dispersive and Lewis Acid-Base Surface Energy of 2D Single-Crystalline and Polycrystalline Covalent Organic Frameworks

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A peer-reviewed article of this preprint also exists.

Tayssir Hamieh^*

This version is not peer-reviewed

Abstract

This paper is devoted to an accurate determination of the London dispersive and polar free energy of adsorption, the two Lewis acid γs+ and base γs- components of polar surface energy γsAB of 2D single-crystalline and polycrystalline covalent organic frameworks such as TAPPy-TPA-COFs. Inverse gas chromatography (IGC) at infinite dilution was used to quantify the different surface parameters of the different materials. From IGC measurements, one determined the net retention time of the adsorption of n-alkanes and several polar solvents on single-crystalline and polycrystalline covalent organic frameworks. The free surface Gibbs energy of adsorption was obtained for the various organic molecules at different temperatures from their net retention volume values. The separation between the London dispersive energy and the polar energy of adsorbed molecules was carried out by using a new thermodynamic parameter PSX chosen as new indicator variable and taken into account the deformation polarizability and the harmonic mean of the ionization energies of solvents and solid materials, derived from London dispersion equation. The obtained results are very promising for the accurate determination of the surface thermodynamic parameters of adsorption of organic solvents on solid surfaces.

Keywords:

Subject: Chemistry and Materials Science - Chemical Engineering

1. Introduction

Covalent organic frameworks (COFs), discovered by Yaghi et al. [1] in 2005 are very interesting crystalline organic porous materials exhibiting very important surface properties concerning their large specific surface area, porosity [2]. Many research works on COFs and their synthesis were developed, due to their aptitude to be used as excellent materials in various applications such as catalysis [3,4,5,6,7], Rechargeable Batteries [8,9,10], separation processes [11], light-emitting materials [12], biomedicine, biosensors and bioelectronics [13,14].

Some promising covalent organic frameworks, such as two-dimensional 2D-COFs composed of 2D-layered polymers, exhibited excellent thermal conductivity [15] and heterogeneous catalytic activity [16]. Two-dimensional imine-based covalent organic framework, single-crystalline and polycrystalline TAPPy-TPA-COF synthetized from 4,4′,4″,4‴-(pyrene-1,3,6,8-tetrayl) tetraaniline (TAPPy) and terephthalaldehyde (TPA), were recently studied by several authors [17,18,19,20,21,22]. The physicochemical properties of 2D-COFs were studied by inverse gas chromatography at infinite dilution by Natraj et al. [18] and Yusuf et al. [19].

One proposed, in this paper, to determine the London dispersive, polar free energy, the two Lewis acid

γ_{s}^{+}

and base

γ_{s}^{-}

components of polar surface energy

γ_{s}^{A B}

of 2D single-crystalline and polycrystalline covalent organic frameworks such as TAPPy-TPA-COFs. The used technique was the inverse gas chromatography (IGC) at infinite dilution [23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41] based on the experimental determination of the net retention time

t_{n}

and volume

V_{n}

of several organic molecules adsorbed on the solid materials. The fundamental thermodynamic equation of IGC allowing to obtain the free energy of adsorption

∆ G_{a}^{0}

of any organic solvents on a solid surface was given in infinite dilution by the following equation:

∆ G_{a}^{0} = - R T l n V_{n} + R T l n (\frac{{s m π}_{0}}{P_{0}})

(1)

where T is the absolute temperature of the chromatographic column containing the solid material, R the prefect gas constant, m is the mass of the solid material of a specific surface area s, and

π_{0}

and

P_{0}

are two reference characteristics respectively referred to the two-dimensional state and atmospheric pressure.

In the case of non-polar solvents such as n-alkanes, the only free energy of adsorption is that of the London dispersion component

∆ G_{a}^{d}

given by:

∆ G_{a}^{0} = ∆ G_{a}^{d}

(2)

For polar organic molecules, one has to add the specific free energy

∆ G_{a}^{s p}

of adsorption:

∆ G_{a}^{0} = ∆ G_{a}^{d} + ∆ G_{a}^{s p}

(3)

Many methods and models were proposed in literature [23,24,25,26,27,28,29,30,31,32,33,34] to determine

∆ G_{a}^{s p}

of polar solvents adsorbed on solid materials and the London dispersive surface energy

γ_{s}^{d}

of the studied materials. The values of

∆ G_{a}^{s p}

and

γ_{s}^{d}

obtained by the various chromatographic methods are very different and strongly depend on the used molecular model and IGC methods. In previous papers, one showed that the surface area of organic molecules not only depends on the chosen molecular surface areas of molecules but also on the temperature [32,33,34,35,36,37] and this affects the different surface thermodynamic parameters. On the other hand, even if we previously proposed the expressions of the surface area of organic molecules and corrected the calculation of

γ_{s}^{d}

of solids, the expressions of these surface areas cannot be always transferred to any other solid.

In a recent paper [42], one proposed a new method based on that of the London dispersion expression [43] by using a new thermodynamic parameter

P_{S X}

dependent both on the deformation polarizability

α_{0 X}

of the probe and on the ionization energies of the solid

ε_{S}

and the solvent

ε_{X}

P_{S X} = \frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})} α_{0 X}

(4)

This method using the equation of the London dispersion interaction [43] was used to better quantify the different Lewis acid-base contributions of the surface energy single-crystalline and poly-crystalline TAPPy-TPA-COFs as well as their polar surface energy.

2. IGC Method and materials

The chromatographic measurements obtained in other studies [18,19,44] led to determine the free energy of adsorption

∆ G_{a}^{0}

R T l n V_{n}

of the adsorbed molecules on the solid substrates as a function of the temperature. The proposed method is that using the deformation polarizability

α_{0 X}

of the adsorbed molecule and the harmonic mean of the ionization energies, given by relation (5):

∆ G_{a}^{0} (T) = - \frac{α_{0 S}}{H^{6}} [\frac{3 N}{{2 (4 π ε_{0})}^{2}} (\frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})} α_{0 X})] + ∆ G_{a}^{s p} (T)

(5)

where and

N

is the Avogadro’s number,

ε_{0}

the permittivity of vacuum, S denoting the solid particle, X the solvent molecule separated by a distance

H

By choosing

P_{S X} = \frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})} α_{0 X}

as thermodynamic parameter and taking the adsorption of n-alkanes on the solid material, one can write the following equation (6):

R T l n V n (n - a l k a n e) = A [\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S X (n - a l k a n e)}] - C

(6)

where

C

is an interaction constant of the adsorbed molecule and

A

is given by:

A = \frac{α_{0 S}}{H^{6}}

(7)

The variations of

R T l n V n (n - a l k a n e)

as a function of

\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S X (n - a l k a n e)}

gave a straight-line called “n-alkanes straight-line”

In the case of polar molecule X, one deduced the specific or polar free energy of interaction between the adsorbed molecule and the solid surface from equation (8) at a temperature T:

(- ∆ G_{a}^{s p} (T)) = R T l n V n (X) - A [\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S - X}] + C

(8)

The determination of

(- ∆ G_{a}^{s p} (T))

versus the temperature and obtain led to obtain the specific enthalpy

(- ∆ H_{a}^{s p})

and entropy

(- ∆ S_{a}^{s p})

of polar solvents, and therefore the Lewis’s acid base constants K_A and K_D by using equation (9):

(- ∆ H^{S p}) = K_{A} \times D N + K_{D} \times A N

(9)

where AN and DN are respectively the electron donor and acceptor numbers of the polar molecule calculated by Gutmann [45] and corrected by Fowkes [46].

Several organic solvents were used in this study: the n-alkanes composed by n-pentane, n-hexane, n-heptane and n-octane whereas the polar probes were the following: Lewis’s acid such as dichloromethane, basic such as ethyl acetate, diethyl ether, tetrahydrofuran and amphoteric such as acetonitrile. The experimental conditions of IGC technique were identical to those given in previous published papers [32,33,34,35].

3. Experimental results

3.1. Polar surface interactions between solid materials and organic molecules

On Table 1, one gave the different values of

α_{0 X}

and

P_{S X}

of the various organic solvents and their ionization energy obtained from the Handbook of Physics and Chemistry [47].

The values of the harmonic mean of ionization energies and parameter

\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S - X}

were presented on Table 2.

By using the values presented on Table 1 and Table 2, one obtained the values of the polar free surface energy (

- ∆ G_{a}^{s p} (T)

) of the polar solvents adsorbed on single-crystalline and poly-crystalline TAPPy-TPA-COFs as a function of the temperature T. On gave the obtained results on Table 3.

The values given on Table 3 showed that the polycrystalline TAPPy-TPA-COFs exhibited higher acid-base interactions than single-crystalline TAPPy-TPA-COFs for all polar solvents with an increasing amphoteric character.

Now, the polar surface energy of interaction

γ_{S - X}^{p} (T)

reflecting the polarity of the adsorbate X was directly calculated from the values of (

- ∆ G_{a}^{s p} (T)

) given on Table 3 by using the values of the surface areas of polar molecules as a function of the temperature given by Hamieh thermal model [32,33,34,35,36,37]. The obtained results for the two COFs were presented on Table 4.

Table 4 showed that the polar surface energy of interaction

γ_{S - X}^{p}

of polar molecules adsorbed on polycrystalline TAPPy-TPA-COFs is about 1.5 times greater than that of single-crystalline TAPPy-TPA-COFs for the different molecules and at any temperature. A decrease of

γ_{S - X}^{p}

of the various polar solvents was observed when the temperature increases. The values on Table 4 proved that the largest polar surface interaction was obtained with acetonitrile followed by tetrahydrofuran and ethyl acetate. This is certainly due to the presence of π-electron-rich triple bond that could enhance π−π interactions between acetonitrile and the two COFs and free pairs of electrons in tetrahydrofuran and ethyl acetate molecules.

3.2. Lewis’s acid and base surface energies of COFs

The Van Oss’s relation was used to determine the Lewis acid

γ_{s}^{+}

and base

γ_{s}^{-}

surface energies of the two COFs. Van Oss et al. proposed [48] the following equation:

- ∆ G_{a}^{s p} (T) = 2 N a (\sqrt{γ_{l}^{-} γ_{s}^{+}} + \sqrt{γ_{l}^{+} γ_{s}^{-}})

(10)

where

γ_{l}^{+}

and

γ_{l}^{-}

are the respective acid-base contributions of the Lewis base surface energy of the solvent adsorbed on COFs.

The two monopolar solvents used were ethyl acetate (EA) and dichloromethane (CH₂Cl₂) respectively characterized by

γ_{E A}^{+} = 0, γ_{E A}^{-} = 19.2 m J / m^{2}

and

γ_{C H 2 C l 2}^{+} = 5.2 m J / m^{2}, γ_{C H 2 C l 2}^{-} = 0

. This led to the determination of the Lewis’s acid and base surface energies of the COFs by using relations (11):

\{\begin{matrix} \begin{matrix} γ_{s}^{+} = \frac{{[∆ G_{a}^{s p} (T) (E A)]}^{2}}{{4 N}^{2} {[a (E A)]}^{2} γ_{E A}^{-}} \end{matrix} \\ γ_{s}^{-} = \frac{{[∆ G_{a}^{s p} (T) (C H 2 C l 2)]}^{2}}{{4 N}^{2} {[a (C H 2 C l 2)]}^{2} γ_{C H 2 C l 2}^{+}} \end{matrix}

(11)

The values of

∆ G_{a}^{s p} (T) (E A)

and

∆ G_{a}^{s p} (T) (C H 2 C l 2)

as a function of the temperature are given by Table 3, whereas, the surface area

a (E A)

and

a (C H 2 C l 2)

are taken from reference []. Furthermore, the total acid-base surface energy

γ_{s}^{A B}

of the two COFs was obtained from relation (12).

γ_{s}^{A B} = 2 \sqrt{γ_{s}^{+} γ_{s}^{-}}

(12)

Relations (11) and (12) allowed to determine the values of

γ_{s}^{+}

γ_{s}^{-}

and

γ_{s}^{A B}

of single-crystalline and polycrystalline TAPPy-TPA-COFs. The results were given on Table 5.

Table 5 showed that the highest values of the polar acid and base surface energies were obtained for polycrystalline TAPPy-TPA-COF, whereas, those of single-crystalline TAPPy-TPA-COF are very weak proving the non-polar character of this material. This result confirmed that obtained when determining the specific free energy of adsorption on the two COFs and their polar surface energy of interaction

γ_{S - X}^{p} (T)

. One also observed that total acid-base surface energy

γ_{s}^{A B}

of polycrystalline TAPPy-TPA-COF is 5 times larger than that of single-crystalline TAPPy-TPA-COF with more accentuated value of the basic surface energy

γ_{s}^{-}

. However, one found approximately identical values for the acid surface energy of materials. It was observed a decrease of the different acid-base components of COFs when the temperature increases.

By using our thermal model, one determined the values of the dispersive component of the surface energy of the two COF materials as a function of the temperature. These values were given on Table 6. The values of

γ_{s}^{A B}

from Table 5 allowed to obtain the total surface energy

γ_{s}^{L W}

also called Lifshitz – Van der Waals (LW) surface energy of single-crystalline and polycrystalline TAPPy-TPA-COFs by using relation (13).

γ_{s}^{L W} = {γ_{s}^{d} + γ}_{s}^{A B}

(13)

The results of Table 6 showed that the polycrystalline TAPPy-TPA-COF surface exhibited higher dispersive, polar and total surface energies about 1.5 times greater than those of the single-crystalline TAPPy-TPA-COF material.

3.3. Lewis’s acid-base parameters

The values of

∆ G_{a}^{s p} (T)

of the various polar molecules given on Table 3 as a function of the temperature allowed to obtain their polar or specific enthalpy (

- ∆ H_{a}^{s p})

and entropy (

- ∆ S_{a}^{s p})

of adsorption on the two COFs. Table 7 gave the obtained results.

The previous results concerning the polarity of the two studied COFs were here confirmed by the values on Table 7 of the polar enthalpy of adsorption of the polar solvents. One observed that all values of (

- ∆ H_{a}^{s p})

of adsorption on the polycrystalline TAPPy-TPA-COF were greater than the single-crystalline TAPPy-TPA-COF.

In order to better understand the Lewis acid-base behavior of the two COF surfaces, one determined the acid-base parameters following equation (9) and results on Table 7. On Figure 1, one plotted the variations

(\frac{- ∆ H_{a}^{s p}}{{A N}^{'}})

as a function of

(\frac{{D N}^{'}}{{A N}^{'}})

of polar molecules adsorbed on the two COFs. The straight-line obtained exhibited two different slopes showing a difference between the Lewis acid-base constants of the studied materials and especially larger acidic constant for polycrystalline surface. The obtained results were given on Table 8.

Table 8 clearly showed the Lewis amphoteric character of the single and polycrystalline COFs with a greater Lewis basicity for the single-crystalline TAPPy-TPA-COF surface and greater Lewis acidity for the polycrystalline TAPPy-TPA-COF surface. It was also observed that

\frac{K_{A} (P o l y c r y s t a l l i n e C O F)}{K_{A} (S i n g l e - c r y s t a l l i n e C O F)} = 1.48

and

\frac{K_{D} (P o l y c r y s t a l l i n e C O F)}{K_{D} (S i n g l e - c r y s t a l l i n e C O F)} = 0.96

that the polycrystalline COF surface was more acidic than the single-crystalline COF surface, whereas, their basicity was comparable. The same results were confirmed by the Lewis entropic acid-base parameters.

The obtained results of the Lewis acid-base constants of the two COFs one again confirmed those obtained for the polar enthalpy and acid-base surface energies of the single and polycrystalline surfaces.

3.4. Consequences and discussion of the new results on COF surfaces

3.4.1. London dipersiveand polar energies of interaction

The new proposed parameter

P_{S X} = \frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})} α_{0 X}

allowed a net separation between the London dispersion energy and the polar free energy of the adsorption of polar organic molecules and COF surfaces. The new method quatified the London dipersive energy of interaction for both n-alkanes by suing relation (14)

∆ G_{a}^{d} (T) = A [\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S X}]

(14)

By applying relation (14), one obtained both the London dispersive and polar free energies of all solvents. The results of London dispersion interactions were presented on Table 9.

Table 9 also showed the higher values of the London dispersion inetractions of the polycrystalline TAPPy-TPA-COF than those obtained with the single-crystalline e TAPPy-TPA-COF for all used organic molecules and all temperatures. The results of Table 9 allowed to obtain the London dispersive enthalpy and entropy of interaction for the two COFs. The obtained values were given on Table 10.

One observed that the values of all dispersive and polar parameters of polycrystalline TAPPy-TPA-COF surface were greater than that of single-crystalline TAPPy-TPA-COF surface.

The results on Table 10 allowed to draw on Figure 2 the variations of London dispersion enthalpie (

- ∆ H_{a}^{d})

as a function of London dispersion entropy (

- ∆ S_{a}^{d})

for the two COFs and the variations corresponding to polar or specific variables of adsorption. A perfect linearity (with R²= 1) was observed. The obtained straight lines werere given below.

In the case of single-crystalline TAPPy-TPA-COF (SC) one obtained equation (15), whereas equation (16) was given for polycrystalline TAPPy-TPA-COF (PC) and

(- ∆ H_{a}^{d} i n k J {m o l}^{- 1}) (S C) = 0.7046 (- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}) (S C) + 0.0501

(15)

(- ∆ H_{a}^{d} i n k J {m o l}^{- 1}) (P C) = 0.6622 (- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}) (P C) - 0.0201

(16)

On also drew on Figure 1 the evolution the specific enthalpy as a function of the specific entropy and obtained the following equations:

(- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}) (S C) = 0.643.6 (- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}) (S C) - 2.0455

(17)

(- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}) (P C) = 0.5978 (- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}) (P C) - 0.8168

(18)

These results conducted us to propose in both cases of dispersion and polar enthalpies and entropies the general equations (19) and (20) relative to the respective dispersion and polar cases:

(- ∆ H_{a}^{d}) (X) = T_{S}^{d} (- ∆ S_{a}^{d}) (X) + (- ∆ G_{a}^{d} (S))

(19)

(- ∆ H_{a}^{s p}) (X) = T_{S}^{d} (- ∆ S_{a}^{s p}) (X) + (- ∆ G_{a}^{s p} (S))

(20)

where

T_{S}^{d}

and

(- ∆ G_{a}^{d} (S))

are two new characteritics of solid substrate respectively representing a dispersion temperature and free dispersion energy of the solid and

T_{S}^{s p}

and

(- ∆ G_{a}^{s p} (S))

those corresponding to the polar interation of the solid. One deduced that every solid surface can be charcterized by two dispersion parameters

T_{S}^{d}

and

(- ∆ G_{a}^{d} (S))

and two ploar parameters

T_{S}^{s p}

and

(- ∆ G_{a}^{s p} (S))

By combining the two dispersion and polar effects, one obtained the following relations:

(- ∆ H_{a}^{d, s p} i n k J {m o l}^{- 1}) (S C) = 0.7553 (- ∆ S_{a}^{d, s p} i n J K^{- 1} {m o l}^{- 1}) (S C) - 3.6943

(21)

(- ∆ H_{a}^{d, s p} i n k J {m o l}^{- 1}) (P C) = 0.6879 (- ∆ S_{a}^{d, s p} i n J K^{- 1} {m o l}^{- 1}) (P C) - 2.7881

(22)

Table 10 and Figure 2 led to give the results of Table 11 these four characteristics for the two COFS.

These new findings deserve more reflection and deepening. One observed that the dispersion temperature is less than the polar temperature for the two COFs. However, the dispersion temperature is greater in the case of single-crystalline COF. The same result was obtained with the polar temperature. One gave on Table 11 the values of the intrinsic temperature

T_{S}

and free energy

(- ∆ G_{a} (S))

of the materials. One found that that

T_{S} (S C) = 755.3 K

and

T_{S} (P C) = 687.9 K

showing that the higher intrinsic temperature was obtained by the single-crystalline COF with a difference between the two temperatures equal to 67.4K. These values will be probably related to the melting point or decomposition temperature of materials.

3.4.2. Comparison with the values obtained by using Donnet et al. method [27]

In order to comapre between our results and those obtained when using Donnet et al. method [27], one gave on Table 12 the values of specific free energy of polar solvents adsorbed on single-crystalline and polycrystalline surfaces.

The comparison between our results and those obtained by using Donnet et al. method [27] (Table 3 and Table 12) showed very large difference due to the insufficiency of the approach proposed by Donnet et al. [27] that neglected the role of the harmonic mean of the ionization energies of organic molecules and solid surface. One observed that the results on Table 12 clearly showed a large difference between the values obtained by the

\frac{(- ∆ G_{a}^{s p} (D o n n e t e t a l .)}{(- ∆ G_{a}^{s p} (H a m i e h))}

reaches for some polar molecules 1.7. Furthermore, a negative value of the specific free energy of dichloromethane was obtained by Donnet et al. method. This negative value of (

- ∆ G_{a}^{s p} (T)

) cannot be acceptable for polar molecule. This resulted from the large approximation used by Donnet et al. two above methods. The same observations was showed for the ratios

\frac{(- ∆ S_{a}^{s p} (D o n n e t e t a l .)}{(- ∆ S_{a}^{s p} (H a m i e h))}

and

\frac{(- ∆ H_{a}^{s p} (D o n n e t e t a l .)}{(- ∆ H_{a}^{s p} (H a m i e h))}

that varied from 0.6 to 0.8 with also negative values when using Donnet method. These results led to acid-base parameters from Donnet al. method completely different from our new approach. Negative values were also obtained for the Lewis baisc constant by using Donnet al. method [27] showing the non-validity of Donnet et al. approach in this case.

3.4.3. Approximative evaluation of the separation distance H between particles

By using the new proposed method, we were able to determine the average separation distance H between the solid particle and the organic moolecule as a function of the temperature. Our results were given on Table 13.

One observed that the average separation distance H weakly varied as a function of the temperature and it is approximately the same for the two COF materials with a distance H comprised between 6.2 and 6.4 Å.

Furthermore, the total potential energy of interaction

I_{T o t .} (r)

between a solid particle and an organic molecule, separated by a distance

r

, is equal to the sum of the repulsive

I_{R e p .} (r)

and Van der Waals attractive

I_{V D W} (r)

energies with their respective interaction constants

A_{R e p .}

and

A_{V D W}

I_{T o t .} (r) = I_{R e p .} (r) + I_{V D W} (r)

(23)

The expressions of

I_{R e p .} (r)

and

I_{V D W} (r)

are respectively given by:

\begin{matrix} I_{R e p .} (r) = \frac{A_{R e p .}}{r^{12}} \\ I_{V D W} (r) = - \frac{A_{V D W}}{r^{6}} \end{matrix}

(24)

And

I_{T o t .} (r)

be then written by the Lennard-Jones equation:

I_{T o t .} (r) = \frac{A_{R e p .}}{r^{12}} - \frac{A_{V D W}}{r^{6}}

(25)

The total potential energy of interaction

I_{T o t .} (r)

is cancelled for

r_{0}

equal to:

r_{0} = {(\frac{A_{R e p .}}{A_{V D W}})}^{1 / 6}

(26)

Whereas,

I_{T o t .} (r)

reaches its minimum energy for a minimal distance H given by:

{H = r}_{m i n .} = {(2 \frac{A_{R e p .}}{A_{V D W}})}^{\frac{1}{6}}

(27)

One obtained relation (28):

r_{0} = \frac{H}{2^{\frac{1}{6}}} \approx 0.891 H

(28)

This allowed to present the obtained results on Table 14.

Table 14 showed a sleight variation of

r_{0}

and the ratio

A_{R e p .} / A_{V D W}

when the temperature varies. One observed a weak decrease of these parameters in the case of polycrystalline surface.

4. Conclusions

The London dispersive and polar surface thermodynamic parameters of single-crystalline and polycrystalline TAPPy-TPA-COFs were determined by inverse gas chromatography technique (IGC) at infinite dilution. One proposed a new method for the separation of London dispersive and polar surface energies. A new intrinsic thermodynamic parameter

P_{S X} = \frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})} α_{0 X}

associating the deformation polarizability of molecules to the harmonic mean of the ionization energies of solid surface and organic molecules. From the measurements of the net retention volume of the adsorbed solvents on COF surfaces, the use of the new parameter

P_{S X}

and by varying the temperature, one obtained the polar interaction energy

∆ G_{a}^{s p} (T)

of the different polar molecules adsorbed on the crystalline and polycrystalline surfaces. This allowed to determine the different components

γ_{s}^{+}

γ_{s}^{-}

γ_{s}^{A B}

of acid-base surface energies of solid surfaces and their total surface energy

γ_{s}^{t o t .}

One showed that all polar or specific surface parameters of the crystalline COF surface were higher than those obtained with the single-crystalline surface. One observed an excellent linearity of

(\frac{- ∆ H_{a}^{s p}}{{A N}^{'}})

versus

(\frac{{D N}^{'}}{{A N}^{'}})

of polar molecules adsorbed on crystalline and polycrystalline surfaces allowing the accurate determination of Lewis’s acid-base constants. The acidity of the polycrystalline surface was proved to be 1.5 times higher than that of the single-crystalline surface.

This new method allowed to determine the dispersive and specific enthalpy and entropy of adsorption, in both cases of single-crystalline (SC) and polycrystalline (PC) and proved that:

(

- ∆ H_{a}^{d, s p}) (X) = T_{S} (- ∆ S_{a}^{d, s p}) (X) + (- ∆ G_{a}^{d, s p} (S))

Two new characteritics of solid substrate

T_{S}

and

(- ∆ G_{a}^{d, s p} (S))

are respectively representing the interaction temperature and free intreaction energy of the solid. One found that that

T_{S} (S C) = 755.3 K

and

T_{S} (P C) = 687.9 K

The comparison of our results with those obtained by Donnet method showed very large difference in the calculations of the specific or polar surface interactions. This resulted from the fact that Donnet method neglected the effect of the harmonic mean of the ionization energies on the different surface thermodynamic parameters.

These new results also allowed to determine an average value of the separation distance between the COF surfaces and the orgnaic molecules.

Funding

This research did not receive any specific grant.

Data Availability Statement

There is no additional data.

Conflicts of Interest

The author declares no conflict of interest.

References

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Figure 1. Variations of

(\frac{- ∆ H_{a}^{s p}}{{A N}^{'}})

as a function of

(\frac{{D N}^{'}}{{A N}^{'}})

of polar molecules adsorbed on crystalline and polycrystalline surfaces.

Figure 1. Variations of

(\frac{- ∆ H_{a}^{s p}}{{A N}^{'}})

as a function of

(\frac{{D N}^{'}}{{A N}^{'}})

of polar molecules adsorbed on crystalline and polycrystalline surfaces.

Figure 2. Variations of London dispersion enthalpie (

- ∆ H_{a}^{d} i n k J {m o l}^{- 1}

) as a function of London dispersion entropy (

- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}

) for the two COFs and the variations corresponding to polar or specific variables (

- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}

) and (

- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}

) of adsorption.

Figure 2. Variations of London dispersion enthalpie (

- ∆ H_{a}^{d} i n k J {m o l}^{- 1}

) as a function of London dispersion entropy (

- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}

) for the two COFs and the variations corresponding to polar or specific variables (

- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}

) and (

- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}

) of adsorption.

Table 1. Values of deformation polarizability (in 10^-30 m³) and (in 10^-40 C m²/V) and ionization energy (in eV) of the various molecules.

Molecule	$ε_{X}$ (eV)	$α_{0}$ (in 10^-30 m³)	$α_{0}$ (in 10^-40 C m²/V)
n-pentane	10.28	9.99	11.12
n-hexane	10.13	11.90	13.24
n-heptane	9.93	13.61	15.14
n-octane	9.80	15.90	17.69
CH₂Cl₂	11.32	7.21	8.02
Diethyl ether	9.51	9.47	10.54
Tetrahydrofuran	9.38	8.22	9.15
Ethyl acetate	10.01	9.16	10.19
Acetonitrile	12.20	4.44	4.94
TAPPy-TPA-COF	7.88	22.38	24.9

Table 2. Values of the harmonic mean of the ionization energies

\frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})}

of TAPPy-TPA-COFs and organic solvents (in 10^-19 J) and the parameter

\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S - X}

(in 10^-15 SI unit) for the various organic molecules.

Table 2. Values of the harmonic mean of the ionization energies

\frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})}

of TAPPy-TPA-COFs and organic solvents (in 10^-19 J) and the parameter

\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S - X}

(in 10^-15 SI unit) for the various organic molecules.

Molecule	$\frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})}$ (in 10^-19J)	$\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S - X}$ (in 10^-15 SI)
n-pentane	7.137	57.886
n-hexane	7.092	68.513
n-heptane	7.030	77.674
n-octane	6.989	90.213
CH₂Cl₂	7.433	43.512
Diethyl ether	6.895	53.010
Tetrahydrofuran	6.852	45.726
Ethyl acetate	7.055	52.462
Acetonitrile	7.660	27.613

Table 3. Values of (

- ∆ G_{a}^{s p} (T)

) (in kJ/mol) of polar molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs.

Table 3. Values of (

- ∆ G_{a}^{s p} (T)

) (in kJ/mol) of polar molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs.

Single-crystalline TAPPy-TPA-COFs
T(K)	393.15	403.15	413.15	423.15
CH₂Cl₂	2.161	2.036	1.719	1.691
Diethyl ether	1.343	1.229	0.966	1.043
THF	5.031	4.879	4.565	4.385
Ethyl Acetate	4.149	3.925	3.683	3.580
Acetonitrile	6.794	6.364	6.069	5.702
Polycrystalline TAPPy-TPA-COFs
T(K)	393.15	403.15	413.15	423.15
CH₂Cl₂	3.317	3.019	3.382	2.998
Diethyl ether	2.245	2.049	1.805	2.024
THF	6.463	5.978	6.302	5.824
Ethyl Acetate	6.058	5.685	5.788	5.443
Acetonitrile	11.426	10.550	10.899	9.892

Table 4. Values of polar surface energy of interaction

γ_{S - X}^{p} (T)

(in mJ/m²) of polar molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs.

Table 4. Values of polar surface energy of interaction

γ_{S - X}^{p} (T)

(in mJ/m²) of polar molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs.

Single-crystalline TAPPy-TPA-COFs
T(K)	393.15	403.15	413.15	423.15
CH₂Cl₂	8.1	7.5	6.2	6.0
Diethyl ether	4.0	3.6	2.8	3.0
THF	21.0	20.3	18.9	18.1
Ethyl Acetate	13.8	13.0	12.1	11.7
Acetonitrile	20.7	19.2	18.1	16.8
Polycrystalline TAPPy-TPA-COFs
T(K)	393.15	403.15	413.15	423.15
CH₂Cl₂	12.5	11.1	12.3	10.7
Diethyl ether	6.7	6.0	5.2	5.8
THF	27.0	24.9	26.1	24.0
Ethyl Acetate	20.2	18.8	19.0	17.7
Acetonitrile	34.7	31.8	32.5	29.2

Table 5. Values of the polar acid and base surface energies

γ_{s}^{+}

γ_{s}^{-}

and

γ_{s}^{A B}

(in mJ/m²) of single-crystalline and polycrystalline TAPPy-TPA-COFs.

Table 5. Values of the polar acid and base surface energies

γ_{s}^{+}

γ_{s}^{-}

and

γ_{s}^{A B}

(in mJ/m²) of single-crystalline and polycrystalline TAPPy-TPA-COFs.

In mJ/m²	Single-crystalline TAPPy-TPA-COF			Polycrystalline TAPPy-TPA-COF
T(K)	$γ_{s}^{-}$	$γ_{s}^{+}$	$γ_{s}^{A B}$	$γ_{s}^{-}$	$γ_{s}^{+}$	$γ_{s}^{A B}$
393.15	2.54	2.07	4.59	7.46	4.42	11.48
403.15	2.21	1.82	4.01	6.37	3.81	9.85
413.15	1.55	1.57	3.11	5.33	3.50	8.63
423.15	1.46	1.45	2.92	4.38	3.19	7.47

Table 6. Values of the dispersive

γ_{s}^{d}

and total

γ_{s}^{t o t .}

surface energies (in mJ/m²) of single-crystalline and polycrystalline TAPPy-TPA-COFs.

Table 6. Values of the dispersive

γ_{s}^{d}

and total

γ_{s}^{t o t .}

surface energies (in mJ/m²) of single-crystalline and polycrystalline TAPPy-TPA-COFs.

In mJ/m²	Single-crystalline TAPPy-TPA-COF		Polycrystalline TAPPy-TPA-COF
T(K)	$γ_{s}^{d}$	$γ_{s}^{L W}$	$γ_{s}^{d}$	$γ_{s}^{L W}$
393.15	66.23	70.82	93.80	105.28
403.15	56.47	60.48	78.18	88.03
413.15	47.47	50.59	69.38	78.01
423.15	38.84	41.75	52.03	59.50

Table 7. Values of (

- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}

) and (

- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}

) of adsorption on the single-crystalline and polycrystalline TAPPy-TPA-COFs.

Table 7. Values of (

- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}

) and (

- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}

) of adsorption on the single-crystalline and polycrystalline TAPPy-TPA-COFs.

Single-crystalline TAPPy-TPA-COF
Polar solvent	$(- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}$ )	$(- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}$ )
CH₂Cl₂	22.1	10.868
Diethyl ether	18.9	8.7816
THF	22.5	13.906
Ethyl acetate	19.5	11.792
Acetonitrile	35.7	20.819
Polycrystalline TAPPy-TPA-COF
Polar solvent	$(- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}$ )	$(- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}$ )
CH₂Cl₂	21.4	11.756
Diethyl ether	22	10.899
THF	35.6	20.404
Ethyl acetate	24.5	15.652
Acetonitrile	59.6	34.712

Table 8. Values of the enthalpic acid base constants

K_{A}

and

K_{D}

and the entropic acid base constants

ω_{A}

and

ω_{D}

of the single-crystalline and polycrystalline TAPPy-TPA-COFs with their corresponding acid base ratios and linear regression coefficients.

Table 8. Values of the enthalpic acid base constants

K_{A}

and

K_{D}

and the entropic acid base constants

ω_{A}

and

ω_{D}

of the single-crystalline and polycrystalline TAPPy-TPA-COFs with their corresponding acid base ratios and linear regression coefficients.

COF surfaces	$K_{A}$	$K_{D}$	$K_{D}$ $/ K_{A}$	$R^{2}$	$10^{3} . ω_{A}$	$10^{3} . ω_{D}$	$ω_{D}$ $/ ω_{A}$	$R^{2}$
Single-crystalline COF	0.149	0.213	1.430	0.947	0.236	0.570	2.413	0.9724
Polycrystalline COF	0.221	0.205	0.930	0.924	0.386	0.358	0.928	0.9361

Table 9. Values of London dispersion interactions (

- ∆ G_{a}^{d} (T) i n k J {m o l}^{- 1}

) of organic molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs.

Table 9. Values of London dispersion interactions (

- ∆ G_{a}^{d} (T) i n k J {m o l}^{- 1}

) of organic molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs.

Single-crystalline TAPPy-TPA-COF
T(K)	393.15	403.15	413.15	423.15
n-pentane	19.861	19.073	18.431	17.962
n-hexane	23.507	22.575	21.815	21.260
n-heptane	26.650	25.593	24.731	24.102
n-octane	30.952	29.725	28.724	27.993
CH₂Cl₂	14.929	14.337	13.854	13.502
Diethyl ether	18.188	17.467	16.878	16.449
Tetrahydrofuran	15.689	15.067	14.559	14.189
Ethyl acetate	18.000	17.286	16.704	16.279
Acetonitrile	9.474	9.098	8.792	8.568
Polycrystalline TAPPy-TPA-COF
T(K)	393.15	403.15	413.15	423.15
n-pentane	23.664	22.471	22.298	20.793
n-hexane	28.008	26.597	26.391	24.610
n-heptane	31.753	30.153	29.920	27.900
n-octane	36.879	35.021	34.750	32.405
CH₂Cl₂	17.788	16.891	16.761	15.630
Diethyl ether	21.671	20.579	20.420	19.041
Tetrahydrofuran	18.693	17.751	17.614	16.425
Ethyl acetate	21.447	20.366	20.209	18.845
Acetonitrile	11.288	10.719	10.636	9.918

Table 10. Values of Values of London dispersion entropy (

- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}

) and enthalpy(

- ∆ H_{a}^{d} i n k J {m o l}^{- 1}

) of organic molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COF surfaces.

Table 10. Values of Values of London dispersion entropy (

- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}

) and enthalpy(

- ∆ H_{a}^{d} i n k J {m o l}^{- 1}

) of organic molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COF surfaces.

COF surfaces	Single-crystalline TAPPy-TPA-COF		Polycrystalline TAPPy-TPA-COF
Dispersion parameters	( $- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}$ )	( $- ∆ H_{a}^{d} i n k J {m o l}^{- 1}$ )	$(- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}$ )	$(- ∆ H_{a}^{d} i n k J {m o l}^{- 1}$ )
n-pentane	63.4	44.702	87.9	58.171
n-hexane	75	52.909	104	68.85
n-heptane	85.1	59.983	117.9	78.056
n-octane	98.8	69.667	136.9	90.657
CH₂Cl₂	47.6	33.602	66.1	43.726
Diethyl ether	58	40.937	80.5	53.271
Tetrahydrofuran	50.1	35.312	69.4	45.951
Ethyl acetate	57.4	40.514	79.6	52.721
Acetonitrile	30.2	21.324	41.9	27.749

Table 11. Values of the new characteristics of single-crystalline and polycrystalline TAPPy-TPA-COF surfaces. These values were directly deduced from relations (15) to (22).

COF surfaces	Single-crystalline TAPPy-TPA-COF	Polycrystalline TAPPy-TPA-COF
$T_{S}^{d}$ (K)	704.6	662.2
$T_{S}^{s p}$ (K)	643.6	597.8
$(- ∆ G_{a}^{d} (S))$ (J/mol)	-50.1	20.1
$(- ∆ G_{a}^{s p} (S))$ (J/mol)	2046	817
$T_{S}$ (K)	755.3	687.9
$(- ∆ G_{a} (S)) (J / m o l)$	3694	2788

Table 12. Values of (

- ∆ G_{a}^{s p} (T)

) (in kJ/mol), (

- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}

) and (

- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}

) of polar molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs by using Donnet et al. method [27].

Table 12. Values of (

- ∆ G_{a}^{s p} (T)

) (in kJ/mol), (

- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}

) and (

- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}

) of polar molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs by using Donnet et al. method [27].

Single-crystalline surface
T(K)	393.15	403.15	413.15	423.15	( $- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}$ )	( $- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}$ )
CH₂Cl₂	-6.994	-6.753	-6.774	-6.586	-12	-11.684
Diethyl ether	2.422	2.268	1.970	2.023	14.9	8.2649
THF	5.271	5.114	4.791	4.607	23.1	14.385
Ethyl Acetate	3.047	2.871	2.663	2.587	15.9	9.2637
Acetonitrile	7.794	7.329	7.001	6.613	38.7	22.982
Polycrystalline surface
T(K)	393.15	403.15	413.15	423.15	( $- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}$ )	( $- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}$ )
CH₂Cl₂	-7.589	-7.334	-6.894	-6.584	-34.6	-21.202
Diethyl ether	3.527	3.272	3.016	3.154	13.7	8.8457
THF	6.744	6.251	6.571	6.076	16.9	13.286
Ethyl Acetate	4.743	4.441	4.551	4.291	12.5	9.5951
Acetonitrile	12.608	11.680	12.019	10.938	46.7	30.864

Table 13. Values of the average separation distance H (in Å) btween the two solid substrates and the organic molecules at different temperatures.

T(K)	393.15	403.15	413.15	423.15
Crystalline surface	6.34	6.39	6.42	6.45
Polycrystalline surface	6.16	6.22	6.22	6.30

Table 14. Values of

r_{0} (i n Å)

and the ratio

A_{R e p .} / A_{V D W} (i n Å^{6})

at different temperatures.

Table 14. Values of

r_{0} (i n Å)

and the ratio

A_{R e p .} / A_{V D W} (i n Å^{6})

at different temperatures.

TAPPy-TPA-COFS	Crystalline surface		Polycrystalline surface
T(K)	$r_{0}$	$A_{R e p .} / A_{V D W}$	$r_{0}$	$A_{R e p .} / A_{V D W}$
393.15	5.65	1.335	5.49	1.328
403.15	5.69	1.336	5.54	1.330
413.15	5.72	1.337	5.54	1.330
423.15	5.75	1.338	5.61	1.333
Average values	5.70	1.34	5.55	1.33

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Submitted:

18 January 2024

Posted:

22 January 2024

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Abstract

Keywords:

Subject: Chemistry and Materials Science - Chemical Engineering

1. Introduction

One proposed, in this paper, to determine the London dispersive, polar free energy, the two Lewis acid

γ_{s}^{+}

and base

γ_{s}^{-}

components of polar surface energy

γ_{s}^{A B}

t_{n}

and volume

V_{n}

of several organic molecules adsorbed on the solid materials. The fundamental thermodynamic equation of IGC allowing to obtain the free energy of adsorption

∆ G_{a}^{0}

of any organic solvents on a solid surface was given in infinite dilution by the following equation:

∆ G_{a}^{0} = - R T l n V_{n} + R T l n (\frac{{s m π}_{0}}{P_{0}})

(1)

where T is the absolute temperature of the chromatographic column containing the solid material, R the prefect gas constant, m is the mass of the solid material of a specific surface area s, and

π_{0}

and

P_{0}

are two reference characteristics respectively referred to the two-dimensional state and atmospheric pressure.

In the case of non-polar solvents such as n-alkanes, the only free energy of adsorption is that of the London dispersion component

∆ G_{a}^{d}

given by:

∆ G_{a}^{0} = ∆ G_{a}^{d}

(2)

For polar organic molecules, one has to add the specific free energy

∆ G_{a}^{s p}

of adsorption:

∆ G_{a}^{0} = ∆ G_{a}^{d} + ∆ G_{a}^{s p}

(3)

Many methods and models were proposed in literature [23,24,25,26,27,28,29,30,31,32,33,34] to determine

∆ G_{a}^{s p}

of polar solvents adsorbed on solid materials and the London dispersive surface energy

γ_{s}^{d}

of the studied materials. The values of

∆ G_{a}^{s p}

and

γ_{s}^{d}

γ_{s}^{d}

of solids, the expressions of these surface areas cannot be always transferred to any other solid.

In a recent paper [42], one proposed a new method based on that of the London dispersion expression [43] by using a new thermodynamic parameter

P_{S X}

dependent both on the deformation polarizability

α_{0 X}

of the probe and on the ionization energies of the solid

ε_{S}

and the solvent

ε_{X}

P_{S X} = \frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})} α_{0 X}

(4)

2. IGC Method and materials

The chromatographic measurements obtained in other studies [18,19,44] led to determine the free energy of adsorption

∆ G_{a}^{0}

R T l n V_{n}

of the adsorbed molecules on the solid substrates as a function of the temperature. The proposed method is that using the deformation polarizability

α_{0 X}

of the adsorbed molecule and the harmonic mean of the ionization energies, given by relation (5):

∆ G_{a}^{0} (T) = - \frac{α_{0 S}}{H^{6}} [\frac{3 N}{{2 (4 π ε_{0})}^{2}} (\frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})} α_{0 X})] + ∆ G_{a}^{s p} (T)

(5)

where and

N

is the Avogadro’s number,

ε_{0}

the permittivity of vacuum, S denoting the solid particle, X the solvent molecule separated by a distance

H

By choosing

P_{S X} = \frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})} α_{0 X}

as thermodynamic parameter and taking the adsorption of n-alkanes on the solid material, one can write the following equation (6):

R T l n V n (n - a l k a n e) = A [\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S X (n - a l k a n e)}] - C

(6)

where

C

is an interaction constant of the adsorbed molecule and

A

is given by:

A = \frac{α_{0 S}}{H^{6}}

(7)

The variations of

R T l n V n (n - a l k a n e)

as a function of

\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S X (n - a l k a n e)}

gave a straight-line called “n-alkanes straight-line”

In the case of polar molecule X, one deduced the specific or polar free energy of interaction between the adsorbed molecule and the solid surface from equation (8) at a temperature T:

(- ∆ G_{a}^{s p} (T)) = R T l n V n (X) - A [\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S - X}] + C

(8)

The determination of

(- ∆ G_{a}^{s p} (T))

versus the temperature and obtain led to obtain the specific enthalpy

(- ∆ H_{a}^{s p})

and entropy

(- ∆ S_{a}^{s p})

of polar solvents, and therefore the Lewis’s acid base constants K_A and K_D by using equation (9):

(- ∆ H^{S p}) = K_{A} \times D N + K_{D} \times A N

(9)

where AN and DN are respectively the electron donor and acceptor numbers of the polar molecule calculated by Gutmann [45] and corrected by Fowkes [46].

3. Experimental results

3.1. Polar surface interactions between solid materials and organic molecules

On Table 1, one gave the different values of

α_{0 X}

and

P_{S X}

of the various organic solvents and their ionization energy obtained from the Handbook of Physics and Chemistry [47].

The values of the harmonic mean of ionization energies and parameter

\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S - X}

were presented on Table 2.

By using the values presented on Table 1 and Table 2, one obtained the values of the polar free surface energy (

- ∆ G_{a}^{s p} (T)

) of the polar solvents adsorbed on single-crystalline and poly-crystalline TAPPy-TPA-COFs as a function of the temperature T. On gave the obtained results on Table 3.

Now, the polar surface energy of interaction

γ_{S - X}^{p} (T)

reflecting the polarity of the adsorbate X was directly calculated from the values of (

- ∆ G_{a}^{s p} (T)

Table 4 showed that the polar surface energy of interaction

γ_{S - X}^{p}

γ_{S - X}^{p}

3.2. Lewis’s acid and base surface energies of COFs

The Van Oss’s relation was used to determine the Lewis acid

γ_{s}^{+}

and base

γ_{s}^{-}

surface energies of the two COFs. Van Oss et al. proposed [48] the following equation:

- ∆ G_{a}^{s p} (T) = 2 N a (\sqrt{γ_{l}^{-} γ_{s}^{+}} + \sqrt{γ_{l}^{+} γ_{s}^{-}})

(10)

where

γ_{l}^{+}

and

γ_{l}^{-}

are the respective acid-base contributions of the Lewis base surface energy of the solvent adsorbed on COFs.

The two monopolar solvents used were ethyl acetate (EA) and dichloromethane (CH₂Cl₂) respectively characterized by

γ_{E A}^{+} = 0, γ_{E A}^{-} = 19.2 m J / m^{2}

and

γ_{C H 2 C l 2}^{+} = 5.2 m J / m^{2}, γ_{C H 2 C l 2}^{-} = 0

. This led to the determination of the Lewis’s acid and base surface energies of the COFs by using relations (11):

\{\begin{matrix} \begin{matrix} γ_{s}^{+} = \frac{{[∆ G_{a}^{s p} (T) (E A)]}^{2}}{{4 N}^{2} {[a (E A)]}^{2} γ_{E A}^{-}} \end{matrix} \\ γ_{s}^{-} = \frac{{[∆ G_{a}^{s p} (T) (C H 2 C l 2)]}^{2}}{{4 N}^{2} {[a (C H 2 C l 2)]}^{2} γ_{C H 2 C l 2}^{+}} \end{matrix}

(11)

The values of

∆ G_{a}^{s p} (T) (E A)

and

∆ G_{a}^{s p} (T) (C H 2 C l 2)

as a function of the temperature are given by Table 3, whereas, the surface area

a (E A)

and

a (C H 2 C l 2)

are taken from reference []. Furthermore, the total acid-base surface energy

γ_{s}^{A B}

of the two COFs was obtained from relation (12).

γ_{s}^{A B} = 2 \sqrt{γ_{s}^{+} γ_{s}^{-}}

(12)

Relations (11) and (12) allowed to determine the values of

γ_{s}^{+}

γ_{s}^{-}

and

γ_{s}^{A B}

of single-crystalline and polycrystalline TAPPy-TPA-COFs. The results were given on Table 5.

γ_{S - X}^{p} (T)

. One also observed that total acid-base surface energy

γ_{s}^{A B}

of polycrystalline TAPPy-TPA-COF is 5 times larger than that of single-crystalline TAPPy-TPA-COF with more accentuated value of the basic surface energy

γ_{s}^{-}

. However, one found approximately identical values for the acid surface energy of materials. It was observed a decrease of the different acid-base components of COFs when the temperature increases.

γ_{s}^{A B}

from Table 5 allowed to obtain the total surface energy

γ_{s}^{L W}

also called Lifshitz – Van der Waals (LW) surface energy of single-crystalline and polycrystalline TAPPy-TPA-COFs by using relation (13).

γ_{s}^{L W} = {γ_{s}^{d} + γ}_{s}^{A B}

(13)

3.3. Lewis’s acid-base parameters

The values of

∆ G_{a}^{s p} (T)

of the various polar molecules given on Table 3 as a function of the temperature allowed to obtain their polar or specific enthalpy (

- ∆ H_{a}^{s p})

and entropy (

- ∆ S_{a}^{s p})

of adsorption on the two COFs. Table 7 gave the obtained results.

- ∆ H_{a}^{s p})

of adsorption on the polycrystalline TAPPy-TPA-COF were greater than the single-crystalline TAPPy-TPA-COF.

(\frac{- ∆ H_{a}^{s p}}{{A N}^{'}})

as a function of

(\frac{{D N}^{'}}{{A N}^{'}})

\frac{K_{A} (P o l y c r y s t a l l i n e C O F)}{K_{A} (S i n g l e - c r y s t a l l i n e C O F)} = 1.48

and

\frac{K_{D} (P o l y c r y s t a l l i n e C O F)}{K_{D} (S i n g l e - c r y s t a l l i n e C O F)} = 0.96

3.4. Consequences and discussion of the new results on COF surfaces

3.4.1. London dipersiveand polar energies of interaction

The new proposed parameter

P_{S X} = \frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})} α_{0 X}

∆ G_{a}^{d} (T) = A [\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S X}]

(14)

By applying relation (14), one obtained both the London dispersive and polar free energies of all solvents. The results of London dispersion interactions were presented on Table 9.

One observed that the values of all dispersive and polar parameters of polycrystalline TAPPy-TPA-COF surface were greater than that of single-crystalline TAPPy-TPA-COF surface.

The results on Table 10 allowed to draw on Figure 2 the variations of London dispersion enthalpie (

- ∆ H_{a}^{d})

as a function of London dispersion entropy (

- ∆ S_{a}^{d})

for the two COFs and the variations corresponding to polar or specific variables of adsorption. A perfect linearity (with R²= 1) was observed. The obtained straight lines werere given below.

In the case of single-crystalline TAPPy-TPA-COF (SC) one obtained equation (15), whereas equation (16) was given for polycrystalline TAPPy-TPA-COF (PC) and

(- ∆ H_{a}^{d} i n k J {m o l}^{- 1}) (S C) = 0.7046 (- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}) (S C) + 0.0501

(15)

(- ∆ H_{a}^{d} i n k J {m o l}^{- 1}) (P C) = 0.6622 (- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}) (P C) - 0.0201

(16)

On also drew on Figure 1 the evolution the specific enthalpy as a function of the specific entropy and obtained the following equations:

(- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}) (S C) = 0.643.6 (- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}) (S C) - 2.0455

(17)

(- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}) (P C) = 0.5978 (- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}) (P C) - 0.8168

(18)

These results conducted us to propose in both cases of dispersion and polar enthalpies and entropies the general equations (19) and (20) relative to the respective dispersion and polar cases:

(- ∆ H_{a}^{d}) (X) = T_{S}^{d} (- ∆ S_{a}^{d}) (X) + (- ∆ G_{a}^{d} (S))

(19)

(- ∆ H_{a}^{s p}) (X) = T_{S}^{d} (- ∆ S_{a}^{s p}) (X) + (- ∆ G_{a}^{s p} (S))

(20)

where

T_{S}^{d}

and

(- ∆ G_{a}^{d} (S))

are two new characteritics of solid substrate respectively representing a dispersion temperature and free dispersion energy of the solid and

T_{S}^{s p}

and

(- ∆ G_{a}^{s p} (S))

those corresponding to the polar interation of the solid. One deduced that every solid surface can be charcterized by two dispersion parameters

T_{S}^{d}

and

(- ∆ G_{a}^{d} (S))

and two ploar parameters

T_{S}^{s p}

and

(- ∆ G_{a}^{s p} (S))

By combining the two dispersion and polar effects, one obtained the following relations:

(- ∆ H_{a}^{d, s p} i n k J {m o l}^{- 1}) (S C) = 0.7553 (- ∆ S_{a}^{d, s p} i n J K^{- 1} {m o l}^{- 1}) (S C) - 3.6943

(21)

(- ∆ H_{a}^{d, s p} i n k J {m o l}^{- 1}) (P C) = 0.6879 (- ∆ S_{a}^{d, s p} i n J K^{- 1} {m o l}^{- 1}) (P C) - 2.7881

(22)

Table 10 and Figure 2 led to give the results of Table 11 these four characteristics for the two COFS.

T_{S}

and free energy

(- ∆ G_{a} (S))

of the materials. One found that that

T_{S} (S C) = 755.3 K

and

T_{S} (P C) = 687.9 K

3.4.2. Comparison with the values obtained by using Donnet et al. method [27]

\frac{(- ∆ G_{a}^{s p} (D o n n e t e t a l .)}{(- ∆ G_{a}^{s p} (H a m i e h))}

reaches for some polar molecules 1.7. Furthermore, a negative value of the specific free energy of dichloromethane was obtained by Donnet et al. method. This negative value of (

- ∆ G_{a}^{s p} (T)

) cannot be acceptable for polar molecule. This resulted from the large approximation used by Donnet et al. two above methods. The same observations was showed for the ratios

\frac{(- ∆ S_{a}^{s p} (D o n n e t e t a l .)}{(- ∆ S_{a}^{s p} (H a m i e h))}

and

\frac{(- ∆ H_{a}^{s p} (D o n n e t e t a l .)}{(- ∆ H_{a}^{s p} (H a m i e h))}

3.4.3. Approximative evaluation of the separation distance H between particles

Furthermore, the total potential energy of interaction

I_{T o t .} (r)

between a solid particle and an organic molecule, separated by a distance

r

, is equal to the sum of the repulsive

I_{R e p .} (r)

and Van der Waals attractive

I_{V D W} (r)

energies with their respective interaction constants

A_{R e p .}

and

A_{V D W}

I_{T o t .} (r) = I_{R e p .} (r) + I_{V D W} (r)

(23)

The expressions of

I_{R e p .} (r)

and

I_{V D W} (r)

are respectively given by:

\begin{matrix} I_{R e p .} (r) = \frac{A_{R e p .}}{r^{12}} \\ I_{V D W} (r) = - \frac{A_{V D W}}{r^{6}} \end{matrix}

(24)

And

I_{T o t .} (r)

be then written by the Lennard-Jones equation:

I_{T o t .} (r) = \frac{A_{R e p .}}{r^{12}} - \frac{A_{V D W}}{r^{6}}

(25)

The total potential energy of interaction

I_{T o t .} (r)

is cancelled for

r_{0}

equal to:

r_{0} = {(\frac{A_{R e p .}}{A_{V D W}})}^{1 / 6}

(26)

Whereas,

I_{T o t .} (r)

reaches its minimum energy for a minimal distance H given by:

{H = r}_{m i n .} = {(2 \frac{A_{R e p .}}{A_{V D W}})}^{\frac{1}{6}}

(27)

One obtained relation (28):

r_{0} = \frac{H}{2^{\frac{1}{6}}} \approx 0.891 H

(28)

This allowed to present the obtained results on Table 14.

Table 14 showed a sleight variation of

r_{0}

and the ratio

A_{R e p .} / A_{V D W}

when the temperature varies. One observed a weak decrease of these parameters in the case of polycrystalline surface.

4. Conclusions

P_{S X} = \frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})} α_{0 X}

P_{S X}

and by varying the temperature, one obtained the polar interaction energy

∆ G_{a}^{s p} (T)

of the different polar molecules adsorbed on the crystalline and polycrystalline surfaces. This allowed to determine the different components

γ_{s}^{+}

γ_{s}^{-}

γ_{s}^{A B}

of acid-base surface energies of solid surfaces and their total surface energy

γ_{s}^{t o t .}

One showed that all polar or specific surface parameters of the crystalline COF surface were higher than those obtained with the single-crystalline surface. One observed an excellent linearity of

(\frac{- ∆ H_{a}^{s p}}{{A N}^{'}})

versus

(\frac{{D N}^{'}}{{A N}^{'}})

This new method allowed to determine the dispersive and specific enthalpy and entropy of adsorption, in both cases of single-crystalline (SC) and polycrystalline (PC) and proved that:

(

- ∆ H_{a}^{d, s p}) (X) = T_{S} (- ∆ S_{a}^{d, s p}) (X) + (- ∆ G_{a}^{d, s p} (S))

Two new characteritics of solid substrate

T_{S}

and

(- ∆ G_{a}^{d, s p} (S))

are respectively representing the interaction temperature and free intreaction energy of the solid. One found that that

T_{S} (S C) = 755.3 K

and

T_{S} (P C) = 687.9 K

These new results also allowed to determine an average value of the separation distance between the COF surfaces and the orgnaic molecules.

Funding

This research did not receive any specific grant.

Data Availability Statement

There is no additional data.

Conflicts of Interest

The author declares no conflict of interest.

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Figure 1. Variations of

(\frac{- ∆ H_{a}^{s p}}{{A N}^{'}})

as a function of

(\frac{{D N}^{'}}{{A N}^{'}})

of polar molecules adsorbed on crystalline and polycrystalline surfaces.

Figure 1. Variations of

(\frac{- ∆ H_{a}^{s p}}{{A N}^{'}})

as a function of

(\frac{{D N}^{'}}{{A N}^{'}})

of polar molecules adsorbed on crystalline and polycrystalline surfaces.

Figure 2. Variations of London dispersion enthalpie (

- ∆ H_{a}^{d} i n k J {m o l}^{- 1}

) as a function of London dispersion entropy (

- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}

) for the two COFs and the variations corresponding to polar or specific variables (

- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}

) and (

- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}

) of adsorption.

Figure 2. Variations of London dispersion enthalpie (

- ∆ H_{a}^{d} i n k J {m o l}^{- 1}

) as a function of London dispersion entropy (

- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}

) for the two COFs and the variations corresponding to polar or specific variables (

- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}

) and (

- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}

) of adsorption.

Table 1. Values of deformation polarizability (in 10^-30 m³) and (in 10^-40 C m²/V) and ionization energy (in eV) of the various molecules.

Molecule	$ε_{X}$ (eV)	$α_{0}$ (in 10^-30 m³)	$α_{0}$ (in 10^-40 C m²/V)
n-pentane	10.28	9.99	11.12
n-hexane	10.13	11.90	13.24
n-heptane	9.93	13.61	15.14
n-octane	9.80	15.90	17.69
CH₂Cl₂	11.32	7.21	8.02
Diethyl ether	9.51	9.47	10.54
Tetrahydrofuran	9.38	8.22	9.15
Ethyl acetate	10.01	9.16	10.19
Acetonitrile	12.20	4.44	4.94
TAPPy-TPA-COF	7.88	22.38	24.9

Table 2. Values of the harmonic mean of the ionization energies

\frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})}

of TAPPy-TPA-COFs and organic solvents (in 10^-19 J) and the parameter

\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S - X}

(in 10^-15 SI unit) for the various organic molecules.

Table 2. Values of the harmonic mean of the ionization energies

\frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})}

of TAPPy-TPA-COFs and organic solvents (in 10^-19 J) and the parameter

\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S - X}

(in 10^-15 SI unit) for the various organic molecules.

Molecule	$\frac{ε_{S} ε_{X}}{(ε_{S} + ε_{X})}$ (in 10^-19J)	$\frac{3 N}{{2 (4 π ε_{0})}^{2}} P_{S - X}$ (in 10^-15 SI)
n-pentane	7.137	57.886
n-hexane	7.092	68.513
n-heptane	7.030	77.674
n-octane	6.989	90.213
CH₂Cl₂	7.433	43.512
Diethyl ether	6.895	53.010
Tetrahydrofuran	6.852	45.726
Ethyl acetate	7.055	52.462
Acetonitrile	7.660	27.613

Table 3. Values of (

- ∆ G_{a}^{s p} (T)

) (in kJ/mol) of polar molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs.

Table 3. Values of (

- ∆ G_{a}^{s p} (T)

) (in kJ/mol) of polar molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs.

Single-crystalline TAPPy-TPA-COFs
T(K)	393.15	403.15	413.15	423.15
CH₂Cl₂	2.161	2.036	1.719	1.691
Diethyl ether	1.343	1.229	0.966	1.043
THF	5.031	4.879	4.565	4.385
Ethyl Acetate	4.149	3.925	3.683	3.580
Acetonitrile	6.794	6.364	6.069	5.702
Polycrystalline TAPPy-TPA-COFs
T(K)	393.15	403.15	413.15	423.15
CH₂Cl₂	3.317	3.019	3.382	2.998
Diethyl ether	2.245	2.049	1.805	2.024
THF	6.463	5.978	6.302	5.824
Ethyl Acetate	6.058	5.685	5.788	5.443
Acetonitrile	11.426	10.550	10.899	9.892

Table 4. Values of polar surface energy of interaction

γ_{S - X}^{p} (T)

(in mJ/m²) of polar molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs.

Table 4. Values of polar surface energy of interaction

γ_{S - X}^{p} (T)

(in mJ/m²) of polar molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs.

Single-crystalline TAPPy-TPA-COFs
T(K)	393.15	403.15	413.15	423.15
CH₂Cl₂	8.1	7.5	6.2	6.0
Diethyl ether	4.0	3.6	2.8	3.0
THF	21.0	20.3	18.9	18.1
Ethyl Acetate	13.8	13.0	12.1	11.7
Acetonitrile	20.7	19.2	18.1	16.8
Polycrystalline TAPPy-TPA-COFs
T(K)	393.15	403.15	413.15	423.15
CH₂Cl₂	12.5	11.1	12.3	10.7
Diethyl ether	6.7	6.0	5.2	5.8
THF	27.0	24.9	26.1	24.0
Ethyl Acetate	20.2	18.8	19.0	17.7
Acetonitrile	34.7	31.8	32.5	29.2

Table 5. Values of the polar acid and base surface energies

γ_{s}^{+}

γ_{s}^{-}

and

γ_{s}^{A B}

(in mJ/m²) of single-crystalline and polycrystalline TAPPy-TPA-COFs.

Table 5. Values of the polar acid and base surface energies

γ_{s}^{+}

γ_{s}^{-}

and

γ_{s}^{A B}

(in mJ/m²) of single-crystalline and polycrystalline TAPPy-TPA-COFs.

In mJ/m²	Single-crystalline TAPPy-TPA-COF			Polycrystalline TAPPy-TPA-COF
T(K)	$γ_{s}^{-}$	$γ_{s}^{+}$	$γ_{s}^{A B}$	$γ_{s}^{-}$	$γ_{s}^{+}$	$γ_{s}^{A B}$
393.15	2.54	2.07	4.59	7.46	4.42	11.48
403.15	2.21	1.82	4.01	6.37	3.81	9.85
413.15	1.55	1.57	3.11	5.33	3.50	8.63
423.15	1.46	1.45	2.92	4.38	3.19	7.47

Table 6. Values of the dispersive

γ_{s}^{d}

and total

γ_{s}^{t o t .}

surface energies (in mJ/m²) of single-crystalline and polycrystalline TAPPy-TPA-COFs.

Table 6. Values of the dispersive

γ_{s}^{d}

and total

γ_{s}^{t o t .}

surface energies (in mJ/m²) of single-crystalline and polycrystalline TAPPy-TPA-COFs.

In mJ/m²	Single-crystalline TAPPy-TPA-COF		Polycrystalline TAPPy-TPA-COF
T(K)	$γ_{s}^{d}$	$γ_{s}^{L W}$	$γ_{s}^{d}$	$γ_{s}^{L W}$
393.15	66.23	70.82	93.80	105.28
403.15	56.47	60.48	78.18	88.03
413.15	47.47	50.59	69.38	78.01
423.15	38.84	41.75	52.03	59.50

Table 7. Values of (

- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}

) and (

- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}

) of adsorption on the single-crystalline and polycrystalline TAPPy-TPA-COFs.

Table 7. Values of (

- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}

) and (

- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}

) of adsorption on the single-crystalline and polycrystalline TAPPy-TPA-COFs.

Single-crystalline TAPPy-TPA-COF
Polar solvent	$(- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}$ )	$(- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}$ )
CH₂Cl₂	22.1	10.868
Diethyl ether	18.9	8.7816
THF	22.5	13.906
Ethyl acetate	19.5	11.792
Acetonitrile	35.7	20.819
Polycrystalline TAPPy-TPA-COF
Polar solvent	$(- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}$ )	$(- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}$ )
CH₂Cl₂	21.4	11.756
Diethyl ether	22	10.899
THF	35.6	20.404
Ethyl acetate	24.5	15.652
Acetonitrile	59.6	34.712

Table 8. Values of the enthalpic acid base constants

K_{A}

and

K_{D}

and the entropic acid base constants

ω_{A}

and

ω_{D}

of the single-crystalline and polycrystalline TAPPy-TPA-COFs with their corresponding acid base ratios and linear regression coefficients.

Table 8. Values of the enthalpic acid base constants

K_{A}

and

K_{D}

and the entropic acid base constants

ω_{A}

and

ω_{D}

of the single-crystalline and polycrystalline TAPPy-TPA-COFs with their corresponding acid base ratios and linear regression coefficients.

COF surfaces	$K_{A}$	$K_{D}$	$K_{D}$ $/ K_{A}$	$R^{2}$	$10^{3} . ω_{A}$	$10^{3} . ω_{D}$	$ω_{D}$ $/ ω_{A}$	$R^{2}$
Single-crystalline COF	0.149	0.213	1.430	0.947	0.236	0.570	2.413	0.9724
Polycrystalline COF	0.221	0.205	0.930	0.924	0.386	0.358	0.928	0.9361

Table 9. Values of London dispersion interactions (

- ∆ G_{a}^{d} (T) i n k J {m o l}^{- 1}

) of organic molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs.

Table 9. Values of London dispersion interactions (

- ∆ G_{a}^{d} (T) i n k J {m o l}^{- 1}

) of organic molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs.

Single-crystalline TAPPy-TPA-COF
T(K)	393.15	403.15	413.15	423.15
n-pentane	19.861	19.073	18.431	17.962
n-hexane	23.507	22.575	21.815	21.260
n-heptane	26.650	25.593	24.731	24.102
n-octane	30.952	29.725	28.724	27.993
CH₂Cl₂	14.929	14.337	13.854	13.502
Diethyl ether	18.188	17.467	16.878	16.449
Tetrahydrofuran	15.689	15.067	14.559	14.189
Ethyl acetate	18.000	17.286	16.704	16.279
Acetonitrile	9.474	9.098	8.792	8.568
Polycrystalline TAPPy-TPA-COF
T(K)	393.15	403.15	413.15	423.15
n-pentane	23.664	22.471	22.298	20.793
n-hexane	28.008	26.597	26.391	24.610
n-heptane	31.753	30.153	29.920	27.900
n-octane	36.879	35.021	34.750	32.405
CH₂Cl₂	17.788	16.891	16.761	15.630
Diethyl ether	21.671	20.579	20.420	19.041
Tetrahydrofuran	18.693	17.751	17.614	16.425
Ethyl acetate	21.447	20.366	20.209	18.845
Acetonitrile	11.288	10.719	10.636	9.918

Table 10. Values of Values of London dispersion entropy (

- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}

) and enthalpy(

- ∆ H_{a}^{d} i n k J {m o l}^{- 1}

) of organic molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COF surfaces.

Table 10. Values of Values of London dispersion entropy (

- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}

) and enthalpy(

- ∆ H_{a}^{d} i n k J {m o l}^{- 1}

) of organic molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COF surfaces.

COF surfaces	Single-crystalline TAPPy-TPA-COF		Polycrystalline TAPPy-TPA-COF
Dispersion parameters	( $- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}$ )	( $- ∆ H_{a}^{d} i n k J {m o l}^{- 1}$ )	$(- ∆ S_{a}^{d} i n J K^{- 1} {m o l}^{- 1}$ )	$(- ∆ H_{a}^{d} i n k J {m o l}^{- 1}$ )
n-pentane	63.4	44.702	87.9	58.171
n-hexane	75	52.909	104	68.85
n-heptane	85.1	59.983	117.9	78.056
n-octane	98.8	69.667	136.9	90.657
CH₂Cl₂	47.6	33.602	66.1	43.726
Diethyl ether	58	40.937	80.5	53.271
Tetrahydrofuran	50.1	35.312	69.4	45.951
Ethyl acetate	57.4	40.514	79.6	52.721
Acetonitrile	30.2	21.324	41.9	27.749

Table 11. Values of the new characteristics of single-crystalline and polycrystalline TAPPy-TPA-COF surfaces. These values were directly deduced from relations (15) to (22).

COF surfaces	Single-crystalline TAPPy-TPA-COF	Polycrystalline TAPPy-TPA-COF
$T_{S}^{d}$ (K)	704.6	662.2
$T_{S}^{s p}$ (K)	643.6	597.8
$(- ∆ G_{a}^{d} (S))$ (J/mol)	-50.1	20.1
$(- ∆ G_{a}^{s p} (S))$ (J/mol)	2046	817
$T_{S}$ (K)	755.3	687.9
$(- ∆ G_{a} (S)) (J / m o l)$	3694	2788

Table 12. Values of (

- ∆ G_{a}^{s p} (T)

) (in kJ/mol), (

- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}

) and (

- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}

) of polar molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs by using Donnet et al. method [27].

Table 12. Values of (

- ∆ G_{a}^{s p} (T)

) (in kJ/mol), (

- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}

) and (

- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}

) of polar molecules adsorbed on single-crystalline and polycrystalline TAPPy-TPA-COFs by using Donnet et al. method [27].

Single-crystalline surface
T(K)	393.15	403.15	413.15	423.15	( $- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}$ )	( $- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}$ )
CH₂Cl₂	-6.994	-6.753	-6.774	-6.586	-12	-11.684
Diethyl ether	2.422	2.268	1.970	2.023	14.9	8.2649
THF	5.271	5.114	4.791	4.607	23.1	14.385
Ethyl Acetate	3.047	2.871	2.663	2.587	15.9	9.2637
Acetonitrile	7.794	7.329	7.001	6.613	38.7	22.982
Polycrystalline surface
T(K)	393.15	403.15	413.15	423.15	( $- ∆ S_{a}^{s p} i n J K^{- 1} {m o l}^{- 1}$ )	( $- ∆ H_{a}^{s p} i n k J {m o l}^{- 1}$ )
CH₂Cl₂	-7.589	-7.334	-6.894	-6.584	-34.6	-21.202
Diethyl ether	3.527	3.272	3.016	3.154	13.7	8.8457
THF	6.744	6.251	6.571	6.076	16.9	13.286
Ethyl Acetate	4.743	4.441	4.551	4.291	12.5	9.5951
Acetonitrile	12.608	11.680	12.019	10.938	46.7	30.864

Table 13. Values of the average separation distance H (in Å) btween the two solid substrates and the organic molecules at different temperatures.

T(K)	393.15	403.15	413.15	423.15
Crystalline surface	6.34	6.39	6.42	6.45
Polycrystalline surface	6.16	6.22	6.22	6.30

Table 14. Values of

r_{0} (i n Å)

and the ratio

A_{R e p .} / A_{V D W} (i n Å^{6})

at different temperatures.

Table 14. Values of

r_{0} (i n Å)

and the ratio

A_{R e p .} / A_{V D W} (i n Å^{6})

at different temperatures.

TAPPy-TPA-COFS	Crystalline surface		Polycrystalline surface
T(K)	$r_{0}$	$A_{R e p .} / A_{V D W}$	$r_{0}$	$A_{R e p .} / A_{V D W}$
393.15	5.65	1.335	5.49	1.328
403.15	5.69	1.336	5.54	1.330
413.15	5.72	1.337	5.54	1.330
423.15	5.75	1.338	5.61	1.333
Average values	5.70	1.34	5.55	1.33

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London Dispersive and Lewis Acid-Base Surface Energy of 2D Single-Crystalline and Polycrystalline Covalent Organic Frameworks

Abstract

1. Introduction

2. IGC Method and materials

3. Experimental results

3.1. Polar surface interactions between solid materials and organic molecules

3.2. Lewis’s acid and base surface energies of COFs

3.3. Lewis’s acid-base parameters

3.4. Consequences and discussion of the new results on COF surfaces

3.4.1. London dipersiveand polar energies of interaction

3.4.2. Comparison with the values obtained by using Donnet et al. method [27]

3.4.3. Approximative evaluation of the separation distance H between particles

4. Conclusions

Funding

Data Availability Statement

Conflicts of Interest

References

Abstract

1. Introduction

2. IGC Method and materials

3. Experimental results

3.1. Polar surface interactions between solid materials and organic molecules

3.2. Lewis’s acid and base surface energies of COFs

3.3. Lewis’s acid-base parameters

3.4. Consequences and discussion of the new results on COF surfaces

3.4.1. London dipersiveand polar energies of interaction

3.4.2. Comparison with the values obtained by using Donnet et al. method [27]

3.4.3. Approximative evaluation of the separation distance H between particles

4. Conclusions

Funding

Data Availability Statement

Conflicts of Interest

References

MDPI Initiatives

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