Study of Chemical Interactions in Binary mixture water-1,4-dioxane Neighbourhood and Associated Model Approach

We use our results of measurements of the activities coefficients of water and 1,4-dioxane at room conditions to analyse the interactions between molecules of water and 1,4-dioxane in different mixtures. Our study is based on “Neighbourhood Model Approach” at liquid state in correlation with solid state to calculate molar fractions of free molecules of water and of 1,4-dioxane in pure liquid state and to deduce the composition of the various mixtures. We calculate system composition in a basis of associate model (called). This model gives good results to interpreting interactions between molecules of water and of 1,4-dioxane. Our model is inspired by resulting experimental recently published by our team, witch measurements of the enthalpy of mixture: mh (XD), present two maxima for molecular fraction of 1,4-dioxane XD = 0.1438 and XD = 0.7805, which correspond to arrangements between molecules of water and 1,4-dioxane of type WD3.56, and DW5.95 (D: 1,4-dioxaneW: water) We use, for the study of the model suggested, a number of 4 neighbours’ molecules in the first shell surrounding one molecule of water and 6 neighbours’ molecules for one molecule of 1,4-dioxane. Our observations confirm well the results of works of many authors by different technical methods.


Introduction
The unique properties of water 1 can be attributed to the ability of water to form four hydrogen bonds with four other molecules, forming a tetrahedral structure.This local organization can give place to an open hexagonal network shell as well in the liquid phase in the solid phase.In addition, theoretical calculations concerning the stability of the aggregates or "clusters" of the water molecules 2,3 , show that (H2O)6 are the most stable aggregate.This configuration resembles to the shape chair of a molecule of 1,4dioxane.It can integrate in the hexagonal network of the ice (Ih) which appears under the normal conditions.Moreover, other recent studies show that the addition of a non-electrolyte supports the formation of these clusters [4][5][6] .
Generally, it is allowed that a non-electrolyte modifies the local or total structure of water.This phenomenon is still the subject of several theoretical, structural and thermodynamic studies, in order to elucidate the process of mixture and solubility according to nature of the aqueous solution (hydrophobic or hydrophilic) and the concentration of water [7][8][9][10][11] .
This study proposes to contribute to better understanding by precise thermodynamic measurements, the structure of the water-1,4-dioxane mixtures, especially in the mediums rich in water.We want in particular to check the assumption according to which the 1,4-dioxane in spite of its character of a not-polar not-electrolyte (permittivity = 2,235 with 25°C and P = 1atm), does not present a hydrophobic character; on the contrary, it reinforces the total structure of water while being incorporated (like clusters (H2O)6) in the hexagonal network describes higher.
b) The existence of azeotrope at molar fraction XD close to 0,5; thus, reflecting the structure associated (H bond) and quasi-regular (incorporation of the molecules of the 1,4-dioxane in the network) with the studied solutions.The checking of such a model implies also the determination of the molar partial enthalpy and the activity coefficients of water and the 1,4-dioxane according to Raoult [13][14] .In this paper, we continue our earlier works studying 1,4-dioxane-water interactions in binary liquid mixture 15,16,17,18 to understanding the cluster formation using simplistic chemical model 19 .We will use two models, called chemical and physical model 20 as following:

Presentation of models
We describe chemical interactions between molecules in a binary mixture water-1,4-dioxane based on measurements of the activities coefficients (reference to Raoult : pure solvent) at 25 °C given starting from the binary diagram liquid -vapour carried out with atmospheric pressure P = 1 atm , and at the temperature 25.00 °C by using the results of measurements of the enthalpy of mixture 15,16 .
We propose a model in which the interactions are translated by water-water, 1,4-dioxane-1,4dioxane and water-1,4-dioxane associations while resting on the principle of neighbourhood shell and the correlation between liquid state and solid state.Our model is inspired by resulting experimental recently published by our team 15 .Measurements of the enthalpy of mixture: mh (XD), present two maxima for molar fraction of 1,4-dioxane XD = 0.1438 and XD = 0.7805 which correspond to arrangements between molecules of water and 1,4-dioxane of type WD3.56 and DW5.95 (see Figure 1

Introduction of the liquid state properties
The liquid state has intermediate properties between the solid state and vapour state.It was viewed like a state of condensed vapour or decompressed solid.Near the freezing point, except for water and of Bismuth, the density of the liquids is lower than that their corresponding crystals; this property is explainable by the fact that while approaching the freezing point the molecules are arranged to form the crystal perfectly.
The structure of the liquid would be an imperfect crystalline structure where one finds site unoccupied.Many studies of the liquid state [21][22][23][24] confirm in their measurements this reasoning, show that by considering « c »: the number of molecules surrounding one molecule; « c » is smaller in the liquid state « cliq » than in a crystalline state « ccr » and decrease with the increase in temperature.
In the liquid state, we can imagine a number of « c » molecules surround the central molecule with missing one site by comparison with the corresponding crystal.Mobility is varying on this basis (as the theory of the liquids) [25][26][27] .Measurements of heat capacities also clarified the problem of the structure of the liquids [28][29][30][31] .

Determination of the number of neighbours site « c » using the approximation of the potential energy.
When energies of interactions concern only the first layer of coordination, the average value of the potential energy of a molecule surrounded by a number « c » of close molecules is U = (1/2).c.Ф where Ф is the interaction energy of only one pair of the molecules .We estimate cliq the number of molecules at the liquid state and ccr the number of molecules at the crystal state.We will express potential energies at liquid and solid state by following: We deduce the potential energies from fusion and sublimation energies.
In a first approximation, we can consider that: U fusion = Lf (latent heat of fusion) and U sublimation = Ls (latent heat of sublimation) .We obtain: The number of coordination in the liquid state is obtained by estimate starting from ccr, L f and L s (see Table 1).
We also call "physical model" the model seen by an observer located outside the mixture where he saw nW moles of water mixed with nD moles of 1,4-dioxane.The interactions water-1,4dioxane are translated by activities coefficients defined by chemical potentials such as: XD is the total molar fraction in mixture, XD = nD/ ( nD + nW) and XW = 1 -XD, W R and D R are activities coefficients of water and 1,4-dioxane by reference to a pure substance (Raoult).
We will study limit case to the zones very rich in water (XD ≈ 0) and very rich in 1,4-dioxane (XD ≈ 1).

Aqueous zone
In the aqueous zone, we suppose that almost all 1,4-dioxane molecules were in the form of monomer XDq  XD1 and thus the 1,4-dioxane number of moles in the mixture is reduced to the number of free monomers added to the number of the D1Wj complex.

Results and discussion
The adjustment of the remainder (Rest) shows well the dominating existence of the pseudocomplex DW6; a molecule of 1,4-dioxane slips into the water supply network, since the remainder (Rest) is only the molar fraction of DW6 (see Graph 3).
This result was confirmed by measurements of heats of water-1,4-dioxane mixture, which presents a minimum corresponding to the formation of pseudo -complex DW6.The partial molar enthalpy of water for the zone very rich in water is negative and tends for XW = 1 towards -2,5 Kcal/mol.(by decreasing the interval of the XD towards the mixtures very rich in water, the adjustment of the remainder (Rest) lead us to values exceeding much more 6 molecules of water (see Graph 2)).This observation makes us think that the 1,4-dioxane addition involves an agglomeration of molecules of water around the 1,4-dioxane, which depends in fact on the 1,4dioxane/water ratio.
These observations confirm well the results of work of many authors 35,36 : Like G. R. Choppin 37 and Sirotkin 38 by IR (Infra-red -absorption spectrum) which affirm that the addition of 1,4-dioxane to water reinforces the structure of the water, work of Ying Guang Wu 39 which distinguished three critical compositions and four fields of composition XD  0, 13, there is presence of the complexes of the type DWj (j = 6,8).0, 13  XD ; 0,3 there is presence of small clusters formed (D1-3, W7-21), XD  0,3 there is presence of D n (n ≈ 10), and we fine disappearance of the clusters DiWj starting from XD  0,7.
In the same way, the study of water-1,4-dioxane structure and its mixtures by diffraction of the neutrons made by Imre Bako 40 shows that with the composition XD = 0,167, the 1,4-dioxane molecules are incorporated in water edifice (adhesion of 1,4-dioxane to the structure of water).The study made by Toshiyuki Takamuku 41 by the techniques of X-rays diffraction, mass spectrometry and relieving by NMR by zone of composition XD announced the presence of water Wn clusters (n = 6 -43) for XD = 0,01 and by adding 1,4-dioxane until XD = 0,4 the 1,4-dioxane molecules are incorporated to form clusters type DmWn (m = 1 -3, n = 1 -16).Recently study carried by V. Madhurima et al 42 concluded that formation of clathrates is verified through contact angle measurements over various substrates and FTIR spectra.
To recapitulate all these remarks, we say that the phenomenon of mixture proceeds as follows: By adding 1,4-dioxane to the water, 1,4-dioxane molecules leave the network of 1,4dioxane and join the molecules water by hydrogen bonds while forming part of the water supply network and by forming associations of the DmWn type where DW6 is dominating 43 .
The energy result is a cooling of water resulting by too phenomenon: Direct phenomena by a formation of associations between molecules of water and 1,4-dioxane molecules or indirect phenomena effect by the influence on the distribution structured water molecules and interstitial water molecules; this effect is seen in the variation of the densities of mixture and of viscosities.Study of density of the mixture shows that by adding 1,4-dioxane to water, the density increases.It is as if 1,4-dioxane molecules are stored within the cavities of the water.More the water /1,4-dioxane ratio is extremely more the associations' number is large.
In this paper, we showed the importance of formal theory of associated solutions.We used a simple model with few parameters based on "Neighbourhood Model Approach" at liquid state in correlation with solid state, where different aspects of the theory of the association are applied.We obtained microscopic information in a base of chemical-physical study 20 and graph 1) (3.56 and 5.95 are XD/XW and XW/XD for maxima: 3.56 = 0.7805/0.2195and 5.95 = 0.8562/0.1438).D: 1,4-dioxane, W: water.If (3.56  4 and 5.95  6), we will use, thereafter, for the study of the model suggested a number of 4 neighbours' molecules in the first shell surrounding one molecule of water and 6 neighbours' molecules for one molecule of 1,4-dioxane.

Figure 1 a
Figure 1 a): The 6 neighbours' molecules in the first shell surrounding one molecule of 1,4dioxane

6 Graph 3 .
. Graph 3 illustrates Distribution of the species in the mixture water-1,4-dioxane according zone XD = 0 -0,Distribution of the species in the mixture water -1,4-dioxane with XD: Green circles represent D7, Gray crosses represent W5 and Red triangles represent the Rest.The solid lines represent the best adjustments in polynomial form for XDiWj = f(XD).

Table 1 :
Theoretical estimate of the number of coordination for the liquids 32)ccr for dioxane is deduced by Crystallographic data: Crystallographic data relative to 1,4-dioxane32:-Space Group: P21/n for phase I « monoclinical system » -Unit form by mesh: Z=2 -The cell parameters (for phase I) are:-Volume of the mesh: V = 222.9Å 3

Table 3 :
Values of "n" the number of water molecules associated with a 1,4-dioxane molecule found by adjustment.