Thermodynamic investigation of glycol ethers in aqueous sugar alcohol at multiple temperatures

. Understanding the molecular dynamics and intermolecular interaction of liquid mixtures can be greatly aided by ultrasonic study. Sound speed and Density of glycols ethers (phenoxyethanol and butoxyethanol) in solutions of a well-known sugar alcohol (d-Mannitol), were measured using the Anton-Paar (DSA 5000 M) at concentrations of (0.02, 0.06, and 0.10) 𝑚𝑜𝑙 ∙ 𝑘𝑔 −1 and fixed experimental pressures (0.1 MPa) over the entire temperature range (288.15, 293.15, 298.15, 303.15) K. With the experimental data of velocity and density, a number of additional dependent basic acoustic-thermodynamic parameters, namely Vander Waal's constant ( 𝑏 ), intermolecular free length ( 𝐿 𝑓 ), acoustic impedance ( 𝑍 ), adiabatic compressibility ( 𝛽 ), Rao's constant ( 𝑅 ), and Wada's constant ( 𝑊 ) have been evaluated. Through these parameters, interactions between solutes and their solvents are expressed in terms of solute-solvent interactions. Research is also done on the solute's capacity to create or destroy structures in a solvent. The inter-molecular interactions amidst the ternary mixture of glycols ethers and d-mannitol in aqueous medium were analyzed.


Introduction
The use of chemical attains recognition in every sector, which includes medical field and ultrasonic behavior.Ultrasonic techniques are a Non-Destructive Technique (NDT) [1].These techniques are used for various purposes, one of them is the different types of structural changes and molecular interactions present in the binary mixtures.These mixtures have many pharmaceutical and food industry application.Ultrasonic waves widely propagate in the air at the velocity of sound.It propagates in suspensions of soaps, binary and ternary liquid-mixtures, polymers, solids, etc.It has a very wide use in leather and textile industry [2,3].Mannitol, molecular formula C6H12O6, is a sugar alcohol or polyol which is used as sweetener and also in medication It is also called as Mannite and manna sugar.It is similar to sorbitol or xylitol.Mannitol IV belongs to a glass of drugs called Diuretics [4][5][6][7].It helps to increase the production of urine.Mannitol is poorly absorbed by the intestines thus it's a low-calorie sweetener.It is used in the therapy of elevated intracranial pressure in brain trauma as hyperosmolar solution.Mannitol loses a hydrogen ion in aqueous solutions, and makes solution acidic.For this reason, its pH can be adjusted.Mannitol helps the brain cells to dehydrate as it draws the water from the brain cells into the bloodstream and thus reduces the acute brain swelling [8][9][10][11].D-Mannitol is accessible and thrifty, and is gettable in an assortment of granular and powder structures.Mannitol is frequently given along with other diuretics such as furosemide, chlorothiazide.Mannitol is metabolized in the liver and end product over here is glycogen.Mannitol shows hydrophilic nature with water molecules.The molecular association between D-mannitol and water molecules arises due to the hydrogen bonding formation.It has fundamental importance for biological reasons as globular proteins gets stabilized with the help of polyhydroxy compounds [12][13][14].
Phenoxyethanol is an aromatic alcohol, a colorless liquid with a pleasant odor, which is also known as 2-phenoxyethanol.Phenoxyethanol work as antimicrobial and is being widely used in cosmetic products as a preservative.It is efficacious against various bacteria and yeasts.2-Butoxyethanol got approval by Food and Drug Administration (US FDA), to be used as food additives in the both ways direct and indirect, antimicrobial agents, defoamers, stabilizers, preservatives, and adhesives [15][16][17][18].In order to determine the physical and chemical properties of the liquid system, a number of thermodynamic parameters were computed in light of the experimental results.In the chemical, pharmaceutical, and cosmetics sectors, mannitol and glycol ethers are frequently used.The current study intends to clarify the intermolecular interactions that take place in liquid mixtures, offering a chance to evaluate the mixture and investigate various characteristics and qualities that improve the product's quality.By studying the thermodynamics, the optimization of the conditions for processes involving glycol ethers and mannitol solutions, whether it's in manufacturing or other applications can be achieved.Given mannitol's role in the pharmaceutical industry, future investigations might delve deeper into the interaction of glycol ethers in mannitol solutions with biological systems.This could lead to the development of novel drug formulations or therapeutic strategies.As researchers uncover more about the thermodynamics, there's potential for designing smart materials that respond to specific conditions.This could have applications in controlled drug release, responsive sensors, or even adaptive materials in various engineering fields [19][20][21][22].

Materials and Methods
For this investigation, D-Mannitol (182.17   ⁄ ) and glycol ethers (118.17  ⁄ and 138.16   ⁄ )respectively are used.The purity order of the chemicals-≥0.99,which were bought from -Loba Chemical Pvt.Ltd., India.All the solutions used in the measurement have been prepared in distilled water, and was weighed by Sartorius CPA 225D balance with accuracy (±0.00001g).The Anton Paar density sound analyzer (DSA) 5000M was used to measure the liquid density speed of sound at various temperatures (288.15 ,293.15, 298.15 and 303.15)K and constant frequency of 3 MHz It is a two-in-one device which can measure the and density and speed of sound simultaneously.

Results and Discussion
Ultrasonic velocity (c) and density () measurements are performed at various temperatures and concentrations.Theoretical calculations for determining acoustic parameters can be performed using the following formulas.  (5) By applying the following formulas to the experimental data, the values of acoustic impedance, adiabatic compressibility, Wada's constant, Rao's constant, intermolecular free length, and Van der Waals' constant are determined.
Acoustics impedance is the offered resistance to the ultrasonic wave propagation in a material.It is utilized to calculate the transmission and the acoustic-reflection on the border line of two separate materials which have distinguishable acoustic impedances. =  ×  (1) The experimental findings show that there is a positive correlation between acoustic impedance and concentration.These values are provided in TABLE 1, suggesting the existence of molecular interactions within the aqueous mixture.The linear fluctuation in acoustic impedance, as demonstrated in, is caused by the lack of specific interaction such as complex creation in the binary mixture.The acoustic impedance increases with the increasing concentration of the mannitol, as well as along the entire composition of glycol ether molality and experimental temperature.This indicates a strong intermolecular interaction between solute and solvent molecules in the system at higher concentration and suggests more association between solute and solvent molecules in the system.The graphical representation in FIGURE 1 and 2 visually illustrates this relationship, confirming the presence of molecular interactions in the solution [23][24][25][26].Adiabatic compressibility can be determined by and sound speed and density of the medium using the given mathematical equation- An increase in intermolecular forces that create aggregation of solvent molecules surrounding the solute is indicated by a shift in adiabatic compressibility in polymer solutions.This might affect the structural arrangement of the solution (solutesolvent interactions).As concentration increases, the adiabatic compressibility decreases due to the strong molecular interactions between the solute and solvent molecules.Similarly, the compressibility decreases with rising temperatures.The fluctuation in adiabatic compressibility with concentration for the mannitol-water system.It demonstrates that when glycol ethers are introduced to aqueous mannitol solutions, compressibility decreases with concentration of mannitol.Glycol ethers tends to disperse water molecules' molecular clumping, freeing up dipoles for interaction.A decrease in compressibility results from an increase in cohesive energy due to the increased force of interaction between mannitol and water.The adiabatic compressibility of decreases as the concentration of mannitol in it increases further.Similar behavior is observed across the whole composition of glycol ether molality.The presence of solvent molecules surrounding solute molecules leads to a reduction in the compressibility of the solute, as evident from   Wada's Constant is calculated using the mathematical expression- Here β is Adiabatic Compressibility and ρ is density.As the temperature rises, the density of the solution decreases.However, when Niacin concentration and glycol molality increase, the density also rises.The increase in density with rising concentration is reflected in the decrease of Wada's constant, while the increase in temperature leads to an increase in Wada's constant.These observations indicate the presence of strong solute-solvent interactions in the aqueous solution.TABLE 2 demonstrates how Wada's constant changes with temperature and concentration, highlighting the variations in the interaction between the solute and solvent molecules.As the temperature rises, the molecules come closer together, leading to a decrease in Wada's constant.FIGURE 5 and 6 illustrates how the distance between the solute and solvent molecules decreases as the temperature and concentration increase, suggesting that the molecules are moving closer to each other, implying a strong solute-solvent interaction in the solution [31][32][33][34].
Rao's Constant defines the relation amid velocity of sound (c), the density (ρ) and effective molecular weight (M) of the given compound.Rao's constant does not depend on temperature and it is represented as Rao's constant increases with a rise in temperature, while its value decreases with increased concentrations.The specific values of Rao's constant are presented in  number of components in the solution increases and they become more closely packed together, the interactions between the molecules intensify, leading to the observed changes in Rao's constant with temperature and concentration [29,32,35].Wada and Rao's constants in relation to temperature and concentration.Rao's molar sound velocity, or constant sound velocity, increases as temperature and concentration rise.When concentration and temperature rise, Rao's constant and Wada's constant, or molar compressibility, show increasing trends.This indicates that there are more components available in a given region, which causes the medium to pack closely and increases interactions [26,36].Intermolecular Free Length can be calculated by the Empirical Formula that is given by Jacobson.Mathematically represented as Lϝ = Kҭ (√) (5) Here, β is compressibility of the liquid and KT is Jacobson constant having value 2.0965 × 10 -6 .As the concentration increases, the free length reduces.This phenomenon is attributed to the liquid compression, and the values are listed in Table 3, indicating molecular interactions between the molecules.As depicted in table, the increase in intermolecular cohesion results in strong molecular connections within the mixture.The consistent decrease in free length leads to an increase in sound velocity in the combination.Conversely, when the temperature rises, the free length increases [37,38].The primary factor that determines how ultrasonic velocity varies in solutions is intermolecular free length.It was discovered that the intermolecular free length in this study decreased linearly with concentration.This results from a decrease in compressibility as concentration rises.This demonstrates a substantial interaction between the solvent and solute molecules in the system.Free length first decreases with mannitol concentration, indicating a disturbance in the water structure, and then increases with temperature, demonstrating a strong molecular interaction between the solute and solvent.Strong interaction between solute-solvent molecules was seen, where the interaction was found to increase linearly with temperature.The fluctuation in free length, which is a clear sign of structure development and breakage, or solute-solvent interaction [26,39].Vander Waal Constant is given which is derived using the relation given as: With the experimental data (density and velocity) of aqueous solutions of Biotin with glycol ethers at varying temperatures and concentrations at a constant frequency of 3 MHz is utilized to determine the above-mentioned parameters.With increase in concentrations and temperature acoustic impedance is increasing following a particular linear trend.With increase in concentrations and temperature adiabatic compressibility is showing decreasing trend.Parameters R (Rao's constant) and W (Wada's constant) shows little upsurge as temperature and the concentration is increasing, it looks as if its constant only Waals constant decreasing with increasing temperature and concentrations [40][41][42][43][44][45].

Conclusion
The strong intermolecular interactions among glycol ethers and mannitol's constituent particles are observed.For all temperatures and concentrations, the trend observed in terms of fundamental properties, like density and velocity, was nature wise linear.The calculated properties, including Vander Waal's constant, Wada's constant, adiabatic compressibility, Rao's constant, intermolecular free length and acoustic impedance, all extend linearly with concentration, suggesting the absence of complex forms.The linear fluctuation in acoustic impedance indicates a strong intermolecular interaction between solute and solvent molecules in the system at higher concentration and suggests more association between solute and solvent molecules in the system.Although the adiabatic compressibility demonstrates a trend that is linearly decreasing with an increase in concentration and decreases in temperature, resulting from an increase in cohesive energy due to the increased force of interaction between mannitol and water.When concentration and temperature rise, Rao's constant and Wada's constant, or molar compressibility, show increasing trends.This indicates that there are more components available in a given region, which causes the medium to pack closely and increases interactions.Free length first decreases with mannitol concentration, indicating a disturbance in the water structure, and then increases with temperature, demonstrating a strong molecular interaction between the solute and solvent.Vander Waal's constant also follows a descending pattern that increases along the temperature but decreases with rise in concentration which is due to the absence of bulky molecules inside the mixture.
= density of the mixtures c= speed of sound of the mixtures M= Molar mass of the solute KT= Jacobian's constant (1)

Table 2
, and they are visually depicted in FIGURE7 and 8.As the

TABLE 2 .
Values of Wada's constant, W and Rao's constant, R of glycol ethers in aqueous solution of Mannitol at different temperatures.

TABLE 3 .
Values of Intermolecular free length, (Lf ) and Vander Waal constant (b) of glycol ethers in aqueous solutions of Mannitol at different temperatures.