Volumetric, acoustic, viscometric, calorimetric and spectroscopic studies to elucidate the effects of citrate and tartrate based food preservatives on the solvation behaviors of acidic amino acids at different temperatures

Abstract

The effects of trisodium citrate (TSC) and disodium tartrate (DST) based food preservatives on the hydration behaviors of the amino acids L-aspartic acid (ASP) and L-glutamic acid (GLU) have been studied using thermodynamic, transport, calorimetric and spectroscopic studies. The volumetric, acoustic and viscosity data suggest that hydrophilic–ionic/hydrophilic interactions are predominant in these systems. The calculated parameters are worthwhile for exploring the solutes as structure-breakers, and the solutes undergo pairwise interactions with the co-solutes. The sweetness of both amino acids decreases in the presence of the preservatives. The hydration number and solvation data suggest that these solutes are more hydrated in water. The dominance of dehydration effects in relation to TSC is observed from the positive enthalpy changes in calorimetry studies and the negative chemical shifts in ¹H NMR studies.

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1. Introduction

Food preservation is carried out to maintain the quality and physicochemical properties of raw food.¹ Preservatives are generally additives, which enhance the life spans of foods and drinks through preventing microorganism growth.² As legislation has restricted the use and the levels of some preservatives in different foods, these preservatives must be approved by food safety authorities.³ Organic acids (citric and tartaric acid) are traditional preservatives. Organic acids are added to foods as acidulants, flavorants, or preservatives, inactivating the growth of spoilage microorganisms and foodborne pathogens.⁴ Citric and tartaric acid show various biological activities. They exhibit metal ion complexing properties with amino acids and, thus, they are preferably used for some common applications in food and agricultural industries as sequestrants, antioxidants, etc. The use of disodium tartrate (DST) and trisodium citrate (TSC) as food additives has been approved by the European Food Safety Authority. They have been assigned with the E numbers 335 and 331, respectively, on the list of antioxidants. It has been mentioned in the literature that sodium salts of citrate and tartrate have been used as anticaking agents, flavour enhancers, etc.^5,6 Salts are effective preservatives because they reduce the water activity of foods. As well as their food-related value, DST can extend the range of plant growth promoters and TSC can help in the production of soil amendments for organic crop production.

L-Glutamate and L-aspartate are key molecules in cellular metabolism. Dietary proteins are broken down in humans through digestion into amino acids, which act as metabolic fuel for other functional activities in the body.⁷ Casein, lactalbumin, Promine-D (soy protein), and wheat gluten contain significant amounts of racemized L-aspartic acid (ASP) and L-glutamic acid (GLU).⁸ GLU is an important nonessential amino acid that acts as a neurotransmitter. It is not considered to be an essential nutrient because it can be manufactured in the human body from simpler compounds. GLU is a building block in protein synthesis. This dicarboxylic amino acid is available in a wide variety of foods and is an important molecule for the metabolism of sugars and fats.⁹ It is also used to enhance the flavour of foods.¹⁰ ASP is used for the generation of adenosine triphosphate, which is a required fuel for cell activity.¹¹ Water is ubiquitous in biochemical processes because its presence generates hydrophobic forces.¹² The physicochemical properties of studied solutes have been used to provide insights into hydrophobicity, hydration properties and solute–solvent interactions.¹³ The use of citrate and tartrate based salts, along with other additives, not only makes flavours sharper but also improves the stability of food products in many cases. The present report aims to study the solvation and taste quality behaviors of acidic amino acids (ASP and GLU) in the presence of citrate (TSC) and tartrate (DST) food preservatives.

2. Experimental

2.1. Materials

All the chemicals used in the present study are of high-purity analytical grade. The purity of the studied chemicals is ≥99%. Details relating to the chemicals are given in Table 1. Before using the chemicals, they have all been dried in vacuo over anhydrous CaCl₂.

Table 1 Sources and solubilities of the chemicals used

S. no.	Compound	Structure	Molar mass (g mol^−1)	Source	Purity^a	CAS number	Solubility in water^a (mg ml^−1)
a As provided by the supplier.
1	L-Aspartic acid		133.10	Siso Research Laboratories, India	99%	56–86–0	≈4.5
2	L-Glutamic acid		147.13	Siso Research Laboratories, India	99%	2419–94.5	≈7.5
3	Di-sodium tartrate		230.08	Central Drug House, India	99%	6132–24–7	≈290
4	Tri-sodium citrate		294.10	Siso Research Laboratories, India	99%	6132–04–3	≈92

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2.2. Equipment and procedures

All stock solutions have been prepared using deionised, double-distilled and degassed water with a specific conductance less than 1.3 × 10⁻⁴ S m⁻¹. The solutions were prepared on a mass basis using a Mettler balance (Model: AB265-S) with a precision of ±0.01 mg. The standard uncertainty in molality is ±2.8 × 10⁻⁴ mol kg⁻¹.

2.2.1. Density and speed of sound. The densities and speeds of sound were measured simultaneously using a vibrating-tube digital density and sound velocity meter (DSA 5000M, Anton Paar). The two-in-one instrument is designed with two cells, i.e., a density cell and a sound velocity cell. Both cells have a set temperature, adjusted using a built-in Peltier thermostat (PT-100) having an accuracy of ±0.001 K. The speed of sound is measured via a propagation time technique. Calibration adjustments were performed at 293.15 K with triple-distilled degassed water, and with dry air at atmospheric pressure. The uncertainties in the temperature, density and speed of sound measurements are 0.03 K, 0.06 kg m⁻³ and 0.6 m s⁻¹, respectively.

2.2.2. Viscosity. Viscosities, η, were determined using a suspended level Ubbelohde-type capillary viscometer having temperature stability within ±0.01 K (model: MC 31A Julabo/Germany). Flow time measurements were done using a stopwatch with a resolution of ±0.01 s. The viscometer has been calibrated with deionized, double-distilled and degassed water. The efflux time data for water was recorded at T = 288.15, 298.15, 308.15 and 318.15 K. Final efflux times are the means of at least six readings. The standard uncertainty in viscosity, u(η), on an average basis is ±0.012 mPa s. The reliability of the apparatus was checked through measuring the viscosities of aqueous solutions of glycine at T = 298.15 K, and the results agreed very well with the literature values.¹⁴ The viscosities of pure water have been taken from the literature.¹⁵

2.2.3. Enthalpy of dilution. An isothermal titration calorimeter, (iTC₂₀₀, MicroCal USA) was used to perform calorimetric titrations at 298.15 ± 0.005 K for the determination of enthalpy of dilution values. 100, 250, and 500 mM DST/TSC solutions were added to a sample cell with a capacity of 200 μl and the syringe was filled with 40 μl of 30 mM ASP/GLU. A total of 19 injections of 2 μl of ASP/GLU was titrated into the sample cell containing DST/TSC and the contents of the cell were stirred at a fixed speed of 500 rpm to ensure complete mixing. The time between successive injections was 120 s, which was managed using the software provided with the instrument. The standard uncertainty in the enthalpy values is ±0.5 kJ mol⁻¹.

2.2.4. Chemical shift measurements. ¹H NMR spectra were obtained using a Bruker spectrometer (AVANCE-III, HD 500 MHz) with a probe temperature of 300.15 K. The centre of the HDO signal (4.650 ppm) is considered as the internal reference for the other nuclei. NMR spectra of ASP and GLU in water and in the presence of aqueous solutions of DST and TSC (m_B = 0.1–0.75 mol kg⁻¹) have been studied in 9 : 1 (w/w) H₂O–D₂O solution. From these spectra, the chemical shift changes (Δδ) were recorded.

3. Results and discussion

3.1. Volumetric measurements

3.1.1. Apparent molar Volumes, V_2,ϕ. The densities, ρ, of the studied amino acids (ASP and GLU) as a function of molality (m_A) in water, and in aqueous solutions of DST and TSC at m_B (molality of DST/TSC) values of 0.10, 0.25, 0.50, and 0.75 mol kg⁻¹ over a temperature range from 288.15 to 323.15 K are given in Table 2. The ρ values directly rise with the m_A and m_B values and decrease with T. The ρ values of aqueous DST and TSC solutions are in good agreement with the literature values,^16–23 and a comparison is shown graphically in Fig. 1. The density values of aqueous solutions of ASP and GLU are also in line with the literature values^9,24–28 and are represented in Fig. 2. The variations in the ρ values of ASP in aqueous DST solutions at different temperatures are shown in Fig. 3(a) (density, ρ, versus molality, m_A, for ASP in DST at m_B = 0.1 mol kg⁻¹ as a function of temperature). In the present study, apparent molar volumes, V_2,ϕ, have been calculated from the experimentally measured densities using the relation:

V_2,ϕ = {M/ρ} − {(ρ − ρ₀)/(m_Aρρ₀)} (1)

where ρ and ρ₀ are the densities of the solution and the solvent (H₂O or H₂O + DST/TSC), M is the molar mass, and m_A is the molality of the solute. The V_2,ϕ values are positive for the studied amino acids both in aqueous and in mixed aqueous solutions. The V_2,ϕ values increase with the m_A, m_B and T values. The V_2,ϕ values of the studied solutes in the absence, as well as in the presence, of aqueous solutions of DST and TSC at m_B values of 0.10, 0.25, 0.50, and 0.75 mol kg⁻¹ and at temperatures from 288.15 to 323.15 K are given in ESI Table S1.† A representative plot of V_2,ϕversus m_A for GLU in aqueous TSC solutions at m_B = 0.25 mol kg⁻¹ and different T values is shown in Fig. 3(b).

Fig. 1 (a) Plots of density, ρ, versus molality, m_B, for aqueous solutions of TSC and comparisons with the literature values at different temperatures. (b) Plots of density, ρ, versus molality, m_B, for aqueous solutions of DST and comparisons with the literature values at different temperatures.

Fig. 2 (a) Plots of density, ρ, versus molality, m_A, for aqueous solutions of ASP and comparisons with the literature values at different temperatures. (b) Plots of density, ρ, versus molality, m_A, for aqueous solutions of GLU and comparisons with the literature values at different temperatures.

Fig. 3 Representative plots of: (a) density, ρ, versus molality, m_A, for L-aspartic acid in aqueous DST solutions (m_B = 0.1 mol kg⁻¹) as a function of temperature, T; (b) apparent molar volume, V₂,_ϕ, versus molality, m_A, for L-glutamic acid in aqueous TSC solutions (m_B = 0.25 mol kg⁻¹) as a function of temperature, T; (c) speed of sound, u, versus molality, m_A, for L-aspartic acid in aqueous TSC solutions (m_B = 0.1 mol kg⁻¹) as a function of temperature, T; and (d) viscosity, η, versus molality, m_A, for L-glutamic acid in aqueous DST solutions (m_B = 0.1 mol kg⁻¹) as a function of temperature, T.

Table 2 Densities, ρ, of L-aspartic acid and L-glutamic acid in water and in aqueous solutions of di-sodium tartrate and tri-sodium citrate at T values from 288.15 to 323.15 K and P = 101.3 kPa

m A/mol kg^−1	10^−3·ρ/kg m^−3
	288.15 K	293.15 K	298.15 K	303.15 K	308.15 K	313.15 K	318.15 K	323.15 K
m A is the molality of the solute in water or water + DST/TSC. mB is the molality of DST/TSC in water. Standard uncertainties, u, are u(T) = 0.03 K, u(P) = 0.5 kPa, u(m) = 2.8 × 10^−4 mol kg^−1, u(ρ) = 0.06 kg m^−3.
L-Aspartic acid in water
0.00000	0.999102	0.998224	0.997047	0.995670	0.994040	0.992238	0.990220	0.988069
0.00517	0.999445	0.998547	0.997360	0.995990	0.994375	0.992558	0.990553	0.988378
0.00712	0.999563	0.998665	0.997477	0.996108	0.994492	0.992674	0.990669	0.988494
0.00921	0.999690	0.998791	0.997602	0.996232	0.994617	0.992799	0.990794	0.988618
0.01109	0.999803	0.998904	0.997715	0.996345	0.994729	0.992911	0.990905	0.988729
0.01300	0.999918	0.999018	0.997829	0.996460	0.994843	0.993024	0.991018	0.988842
0.01506	1.000042	0.999141	0.997952	0.996582	0.994965	0.993147	0.991140	0.988964
L-Aspartic acid in an aqueous solution of di-sodium tartrate at mB= 0.1 mol kg^−1
0.00000	1.014500	1.012800	1.010169	1.008856	1.006932	1.004950	1.002974	1.000950
0.00502	1.014789	1.013089	1.010457	1.009144	1.007220	1.005238	1.003261	1.001237
0.00741	1.014926	1.013226	1.010594	1.009280	1.007356	1.005374	1.003398	1.001374
0.01180	1.015178	1.013477	1.010730	1.009531	1.007607	1.005624	1.003648	1.001624
0.01306	1.015249	1.013548	1.010844	1.009603	1.007678	1.005695	1.003719	1.001695
0.01732	1.015492	1.013791	1.010916	1.009845	1.007921	1.005938	1.003960	1.001936
L-Aspartic acid in an aqueous solution of di-sodium tartrate at mB= 0.25 mol kg^−1
0.00000	1.032450	1.030457	1.028594	1.026540	1.025089	1.023450	1.020973	1.018500
0.00584	1.032778	1.030784	1.028920	1.026866	1.025415	1.023775	1.021298	1.018824
0.00817	1.032908	1.030914	1.029050	1.026995	1.025544	1.023904	1.021427	1.018953
0.01106	1.033069	1.031075	1.029211	1.027156	1.025704	1.024064	1.021586	1.019112
0.01337	1.033198	1.031203	1.029338	1.027283	1.025832	1.024191	1.021713	1.019239
0.01555	1.033319	1.031323	1.029459	1.027404	1.025952	1.024311	1.021833	1.019358
0.01667	1.033380	1.031385	1.029520	1.027465	1.026013	1.024372	1.021894	1.019419
L-Aspartic acid in an aqueous solution of di-sodium tartrate at mB= 0.50 mol kg^−1
0.00000	1.063200	1.061500	1.059301	1.057450	1.055350	1.053240	1.050971	1.048200
0.00638	1.063544	1.061843	1.059644	1.057793	1.055692	1.053582	1.051313	1.048542
0.00782	1.063620	1.061920	1.059721	1.057870	1.055769	1.053659	1.051389	1.048619
0.00982	1.063726	1.062027	1.059828	1.057976	1.055876	1.053765	1.051495	1.048725
0.01307	1.063899	1.062200	1.060001	1.058150	1.056049	1.053938	1.051667	1.048897
0.01509	1.064006	1.062307	1.060109	1.058257	1.056156	1.054044	1.051774	1.049004
0.01539	1.064074	1.062375	1.060178	1.058325	1.056225	1.054113	1.051842	1.049072
L-Aspartic acid in an aqueous solution of di-sodium tartrate at mB= 0.75 mol kg^−1
0.00000	1.093900	1.091750	1.090008	1.087450	1.085611	1.083560	1.080970	1.078900
0.00547	1.094183	1.092032	1.090289	1.087731	1.085892	1.083841	1.081250	1.079180
0.00739	1.094282	1.092131	1.090387	1.087829	1.085990	1.083938	1.081348	1.079278
0.01025	1.094429	1.092278	1.090532	1.087975	1.086135	1.084084	1.081493	1.079423
0.01347	1.094595	1.092443	1.090697	1.088138	1.086298	1.084247	1.081656	1.079585
0.01664	1.094758	1.092605	1.090856	1.088298	1.086458	1.084407	1.081816	1.079743
L-Aspartic acid in an aqueous solution of tri-sodium citrate at mB= 0.1 mol kg^−1
0.00000	1.017603	1.01651	1.015194	1.013658	1.011929	1.010035	1.007541	1.005738
0.00576	1.017926	1.016832	1.015515	1.013979	1.012250	1.010356	1.007861	1.006058
0.00754	1.018025	1.016931	1.015614	1.014077	1.012348	1.010454	1.007960	1.006157
0.01002	1.018164	1.017069	1.015752	1.014214	1.012485	1.010592	1.008097	1.006294
0.01189	1.018267	1.017173	1.015855	1.014317	1.012588	1.010695	1.008200	1.006397
0.01520	1.018451	1.017357	1.016038	1.014500	1.012770	1.010878	1.008383	1.006579
L-Aspartic acid in an aqueous solution of tri-sodium citrate at mB= 0.25 mol kg^−1
0.00000	1.044743	1.043390	1.041855	1.040130	1.038238	1.036425	1.033088	1.030213
0.00624	1.045084	1.043730	1.042194	1.040469	1.038576	1.036762	1.033425	1.030549
0.00784	1.045171	1.043816	1.042281	1.040555	1.038662	1.036848	1.033510	1.030635
0.01080	1.045332	1.043976	1.042441	1.040715	1.038821	1.037007	1.033668	1.030794
0.01208	1.045401	1.044045	1.042510	1.040784	1.038889	1.037075	1.033736	1.030862
0.01490	1.045554	1.044197	1.042663	1.040936	1.039040	1.037225	1.033886	1.031012
0.01825	1.045735	1.044377	1.042843	1.041116	1.039218	1.037403	1.034064	1.031189
L-Aspartic acid in an aqueous solution of tri-sodium citrate at mB= 0.50 mol kg^−1
0.00000	1.089975	1.088190	1.086290	1.084250	1.082085	1.078250	1.075665	1.072453
0.00597	1.090285	1.088499	1.086598	1.084557	1.082393	1.078558	1.075973	1.072761
0.00809	1.090395	1.088608	1.086707	1.084666	1.082501	1.078666	1.076081	1.072869
0.00985	1.090485	1.088699	1.086797	1.084757	1.082591	1.078756	1.076171	1.072959
0.01284	1.090639	1.088852	1.086951	1.084910	1.082744	1.078909	1.076323	1.073111
0.01520	1.090760	1.088973	1.087071	1.085030	1.082863	1.079029	1.076443	1.073232
0.01810	1.090908	1.089120	1.087219	1.085177	1.083010	1.079176	1.076589	1.073378
L-Aspartic acid in an aqueous solution of tri-sodium citrate at mB= 0.75 mol kg^−1
0.00000	1.135208	1.132990	1.130725	1.128370	1.125933	1.122547	1.118243	1.115480
0.00626	1.135513	1.133294	1.131029	1.128673	1.126237	1.122852	1.118548	1.115786
0.00788	1.135591	1.133373	1.131107	1.128752	1.126315	1.122930	1.118627	1.115864
0.01082	1.135733	1.133514	1.131249	1.128893	1.126457	1.123073	1.118769	1.116006
0.01180	1.135779	1.133562	1.131296	1.128940	1.126505	1.123120	1.118816	1.116052
0.01461	1.135914	1.133696	1.131431	1.129075	1.126640	1.123255	1.118952	1.116188
0.01732	1.136042	1.133825	1.131560	1.129204	1.126769	1.123384	1.119082	1.116318
L-Glutamic acid in water
0.01104	0.999776	0.998875	0.997680	0.996307	0.994687	0.992865	0.990860	0.988682
0.01308	0.999894	0.998992	0.997796	0.996423	0.994802	0.992978	0.990973	0.988794
0.01522	1.000019	0.999115	0.997919	0.996544	0.994921	0.993096	0.991091	0.988912
0.02078	1.000341	0.999434	0.998235	0.996857	0.995233	0.993404	0.991399	0.989217
0.02517	1.000595	0.999686	0.998485	0.997104	0.995479	0.993645	0.991640	0.989457
0.03030	1.000890	0.999978	0.998775	0.997390	0.995765	0.993927	0.991922	0.988735
L-Glutamic acid in an aqueous solution of di-sodium tartrate at mB= 0.1 mol kg^−1
0.01288	1.015222	1.013518	1.010883	1.009568	1.007642	1.005658	1.003681	1.001656
0.01523	1.015352	1.013648	1.011011	1.009697	1.007770	1.005787	1.003808	1.001782
0.01930	1.015577	1.013873	1.011235	1.009919	1.007992	1.006010	1.004028	1.002001
0.02496	1.015890	1.014184	1.011546	1.010228	1.008300	1.006318	1.004335	1.002307
0.03127	1.016238	1.014530	1.011890	1.010571	1.008642	1.006659	1.004674	1.002645
0.03591	1.016492	1.014782	1.012142	1.010819	1.008890	1.006909	1.004920	1.002892
L-Glutamic acid in an aqueous solution of di-sodium tartrate at mB= 0.25 mol kg^−1
0.01410	1.033219	1.031223	1.029358	1.027302	1.025850	1.024208	1.021730	1.019255
0.01537	1.033286	1.031291	1.029426	1.027369	1.025917	1.024276	1.021797	1.019322
0.01930	1.033499	1.031503	1.029638	1.027580	1.026127	1.024485	1.022006	1.019531
0.02391	1.033747	1.031750	1.029885	1.027826	1.026372	1.024730	1.022250	1.019775
0.03000	1.034075	1.032075	1.030211	1.028150	1.026695	1.025053	1.022572	1.020096
0.03235	1.034200	1.032200	1.030334	1.028271	1.026819	1.025176	1.022695	1.020217
L-Glutamic acid in an aqueous solution of di-sodium tartrate at mB= 0.50 mol kg^−1
0.01228	1.063847	1.062143	1.059940	1.058089	1.055985	1.053871	1.051601	1.048830
0.01354	1.063912	1.062208	1.060005	1.058153	1.056049	1.053935	1.051666	1.048892
0.01654	1.064069	1.062363	1.060160	1.058307	1.056202	1.054088	1.051818	1.049043
0.02018	1.064258	1.062551	1.060347	1.058492	1.056388	1.054274	1.052003	1.049227
0.02585	1.064553	1.062844	1.060638	1.058782	1.056675	1.054561	1.052290	1.049512
0.03703	1.065130	1.063412	1.061210	1.059350	1.057240	1.055124	1.052854	1.050070
L-Glutamic acid in an aqueous solution of di-sodium tartrate at mB= 0.75 mol kg^−1
0.01159	1.094489	1.092337	1.090661	1.087995	1.086187	1.084131	1.081540	1.079468
0.01375	1.094597	1.092445	1.090767	1.088101	1.086294	1.084236	1.081645	1.079572
0.01765	1.094792	1.092640	1.090960	1.088293	1.086486	1.084426	1.081835	1.079760
0.01995	1.094907	1.092755	1.091073	1.088405	1.086599	1.084538	1.081945	1.079870
0.02676	1.095245	1.093095	1.091407	1.088740	1.086931	1.084867	1.082275	1.080198
L-Glutamic acid in an aqueous solution of tri-sodium citrate at mB= 0.1 mol kg^−1
0.01247	1.018281	1.017186	1.015870	1.014333	1.012603	1.010708	1.008213	1.006409
0.01463	1.018396	1.017301	1.015986	1.014449	1.012719	1.010823	1.008329	1.006524
0.01634	1.018487	1.017392	1.016077	1.014541	1.012811	1.010913	1.008420	1.006615
0.02218	1.018800	1.017706	1.016391	1.014854	1.013124	1.011224	1.008729	1.006926
0.02857	1.019140	1.018044	1.016732	1.015194	1.013464	1.011563	1.009067	1.007265
0.03390	1.019423	1.018324	1.017015	1.015478	1.013747	1.011844	1.009348	1.007545
L-Glutamic acid in an aqueous solution of tri-sodium citrate at mB= 0.25 mol kg^−1
0.01213	1.045383	1.044029	1.042489	1.040763	1.038868	1.037053	1.033716	1.030842
0.01438	1.045500	1.044146	1.042605	1.040879	1.038983	1.037169	1.033832	1.030956
0.01771	1.045674	1.044320	1.042778	1.041051	1.039155	1.037340	1.034000	1.031126
0.02308	1.045954	1.044600	1.043055	1.041328	1.039430	1.037615	1.034274	1.031400
0.02531	1.046069	1.044715	1.043170	1.041442	1.039542	1.037728	1.034386	1.031512
0.03401	1.046520	1.045167	1.043619	1.041888	1.039985	1.038168	1.034828	1.031953
L-Glutamic acid in an aqueous solution of tri-sodium citrate at mB= 0.50 mol kg^−1
0.01104	1.090520	1.088735	1.086830	1.084790	1.082623	1.078787	1.076200	1.072989
0.01239	1.090585	1.088800	1.086896	1.084854	1.082687	1.078851	1.076265	1.073054
0.01547	1.090735	1.088950	1.087047	1.085003	1.082836	1.078999	1.076412	1.073202
0.02012	1.090960	1.089176	1.087272	1.085226	1.083059	1.079222	1.076634	1.073426
0.02521	1.091205	1.089423	1.087517	1.085470	1.083303	1.079465	1.076874	1.073670
0.03006	1.091438	1.089657	1.087749	1.085700	1.083535	1.079694	1.077100	1.073900
L-Glutamic acid in an aqueous solution of tri-sodium citrate at mB= 0.75 mol kg^−1
0.01088	1.135703	1.133485	1.131216	1.128861	1.126424	1.123036	1.118734	1.115969
0.01408	1.135848	1.133629	1.131360	1.129005	1.126566	1.123180	1.118877	1.116112
0.01532	1.135903	1.133683	1.131415	1.129059	1.126620	1.123235	1.118932	1.116166
0.02000	1.136113	1.133892	1.131625	1.129267	1.126827	1.123443	1.119140	1.116373
0.02799	1.136469	1.134249	1.131980	1.129622	1.127179	1.123796	1.119494	1.116725
0.03107	1.136605	1.134385	1.132115	1.129756	1.127314	1.123930	1.119629	1.116855

---

3.1.2. Partial molar volumes, V_2,ϕ⁰. The V_2,ϕ⁰ values have been evaluated by fitting the corresponding data to the given equation as follows:

V_2,ϕ = V_2,ϕ⁰ + S_vm (2)

The volumetric virial coefficient, i.e., S_v, is the experimental slope in the given equation. The V_2,ϕ⁰ values and the standard deviation values are tabulated in Table 3. The V_2,ϕ⁰ values for aqueous solutions of amino acids agree well with those reported in the literature (Table 3).^24–30

Table 3 Partial molar volumes, V_2,ϕ⁰, of L-aspartic acid and L-glutamic acid in water and in aqueous solutions of di-sodium tartrate and tri-sodium citrate at T values from 288.15 to 323.15 K and P = 101.3 kPa

m B/mol kg^−1	10^6V2,ϕ^0 m^−3 mol^−1
	288.15 K	293.15 K	298.15 K	303.15 K	308.15 K	313.15 K	318.15 K	323.15 K
a Ref. 24. b Ref. 25. c Ref. 26. d Ref. 27. e Ref. 28. f Ref. 29. g Ref. 30; parentheses contain Sv (m^3 kg mol^−2) values; standard uncertainties, u, are u(T) = 0.03 K, u(p) = 0.5 kPa, u(m) = 2.8 × 10^−4 mol kg^−1.
L-Aspartic acid in an aqueous solution of di-sodium tartrate
0.0	71.73 ± 0.01	72.02 ± 0.04	72.35 ± 0.04	72.55 ± 0.03	72.74 ± 0.01	72.98 ± 0.01	73.25 ± 0.01	73.46 ± 0.02
	71.8^a, 72.21^b	(46.19 ± 5.10)	72.30^a, 73.14^b, 73.34^c, 73.33^d	74.13^c, 74.13^d	72.78^a, 74.17^b, 75.04^c, 75.03^d	76.01^c, 76.01^d	73.23^a	(28.61 ± 2.80)
	(45.37 ± 1.47)		(42.67 ± 4.86)	(34.31 ± 3.92)	(31.06 ± 1.65)	(26.65 ± 1.77)	(28.96 ± 1.71)
0.1	75.06 ± 0.03	75.19 ± 0.02	75.44 ± 0.01	75.50 ± 0.02	75.59 ± 0.02	75.62 ± 0.01	75.68 ± 0.02	75.75 ± 0.02
	(25.48 ± 2.70)	(23.27 ± 2.25)	(12.64 ± 1.18)	(14.64 ± 2.36)	(14.35 ± 1.97)	(17.57 ± 1.30)	(20.99 ± 2.31)	(19.66 ± 2.38)
0.25	76.04 ± 0.02	76.24 ± 0.03	76.48 ± 0.01	76.54 ± 0.01	76.65 ± 0.02	76.74 ± 0.02	76.85 ± 0.01	76.93 ± 0.01
	(26.40 ± 2.07)	(25.89 ± 2.66)	(19.64 ± 1.52)	(23.10 ± 1.49)	(20.60 ± 2.26)	(25.38 ± 1.75)	(26.12 ± 1.01)	(32.56 ± 0.59)
0.50	77.27 ± 0.03	77.39 ± 0.02	77.60 ± 0.03	77.69 ± 0.04	77.75 ± 0.02	77.79 ± 0.02	77.93 ± 0.03	77.98 ± 0.01
	(44.41 ± 3.76)	(34.32 ± 2.84)	(19.91 ± 3.35)	(20.86 ± 4.10)	(24.55 ± 2.27)	(33.46 ± 2.14)	(33.36 ± 3.21)	(32.24 ± 1.61)
0.75	78.46 ± 0.002	78.56 ± 0.02	78.71 ± 0.03	78.82 ± 0.01	78.90 ± 0.008	78.95 ± 0.03	79.11 ± 0.02	79.16 ± 0.01
	(4.23 ± 0.33)	(11.50 ± 1.97)	(27.31 ± 3.02)	(24.49 ± 1.40)	(28.81 ± 0.85)	(31.10 ± 3.68)	(28.16 ± 2.30)	(38.43 ± 1.57)
L-Aspartic acid in an aqueous solution of tri-sodium citrate
0.1	76.51 ± 0.02	76.71 ± 0.01	76.92 ± 0.01	76.98 ± 0.03	77.02 ± 0.03	77.12 ± 0.01	77.22 ± 0.007	77.26 ± 0.01
	(22.38 ± 2.38)	(17.03 ± 1.23)	(16.05 ± 1.44)	(24.68 ± 3.87)	(28.24 ± 3.78)	(15.76 ± 1.46)	(18.43 ± 0.90)	(23.00 ± 1.39)
0.25	77.20 ± 0.005	77.40 ± 0.02	77.61 ± 0.01	77.72 ± 0.01	77.78 ± 0.03	77.95 ± 0.02	78.12 ± 0.05	78.18 ± 0.01
	(17.99 ± 0.52)	(22.63 ± 2.29)	(10.25 ± 1.13)	(12.55 ± 0.90)	(28.84 ± 2.86)	(27.47 ± 2.32)	(31.73 ± 4.68)	(30.23 ± 1.34)
0.50	78.26 ± 0.01	78.48 ± 0.01	78.71 ± 0.01	78.82 ± 0.02	78.84 ± 0.02	79.00 ± 0.02	79.05 ± 0.02	79.11 ± 0.02
	(22.48 ± 1.16)	(20.19 ± 1.23)	(13.71 ± 1.08)	(15.64 ± 2.03)	(25.68 ± 1.57)	(21.00 ± 1.76)	(27.61 ± 1.83)	(28.47 ± 2.25)
0.75	79.23 ± 0.02	79.42 ± 0.01	79.64 ± 0.02	79.75 ± 0.02	79.79 ± 0.02	79.81 ± 0.02	79.88 ± 0.01	79.94 ± 0.03
	(33.88 ± 2.43)	(24.78 ± 1.52)	(17.23 ± 1.73)	(18.05 ± 1.71)	(16.40 ± 2.20)	(18.86 ± 2.20)	(21.13 ± 1.20)	(27.03 ± 3.29)
L-Glutamic acid in an aqueous solution of di-sodium tartrate
0.0	88.34 ± 0.01	88.78 ± 0.04	89.70 ± 0.02	90.01 ± 0.01	90.64 ± 0.03	91.19 ± 0.03	91.46 ± 0.03	91.90 ± 0.02
	88.35^a, 88.88^b	86.68^e	89.65^a, 90.19^b, 87.84^e, 89^f, 90.06^f, 89.64^g, 89.65^g	89.25^e	90.54^a, 91.05^b	89.87^e	91.20^a	90.64^e
	(17.83 ± 0.51)	(22.72 ± 2.42)	(11.13 ± 1.08)	(19.88 ± 0.86)	(12.77 ± 1.80)	(20.83 ± 1.91)	(16.57 ± 1.49)	(18.29 ± 1.26)
0.1	90.37 ± 0.03	90.62 ± 0.01	91.10 ± 0.04	91.23 ± 0.02	91.46 ± 0.03	91.72 ± 0.03	91.86 ± 0.03	92.01 ± 0.06
	(16.23 ± 1.31)	(18.16 ± 0.54)	(14.97 ± 2.09)	(19.55 ± 1.23)	(19.40 ± 1.29)	(13.04 ± 1.30)	(21.12 ± 1.63)	(23.46 ± 2.93)
0.25	91.16 ± 0.03	91.32 ± 0.01	91.57 ± 0.03	91.73 ± 0.04	91.92 ± 0.03	92.17 ± 0.01	92.31 ± 0.02	92.52 ± 0.03
	(13.60 ± 1.74)	(17.47 ± 0.62)	(13.77 ± 1.55)	(18.93 ± 2.12)	(17.61 ± 1.49)	(15.50 ± 0.58)	(17.96 ± 1.29)	(18.35 ± 1.96)
0.50	91.59 ± 0.03	91.86 ± 0.03	92.35 ± 0.02	92.41 ± 0.06	92.75 ± 0.04	93.17 ± 0.01	93.33 ± 0.02	93.49 ± 0.07
	(14.53 ± 1.57)	(20.06 ± 1.32)	(11.94 ± 0.78)	(19.37 ± 2.88)	(18.96 ± 1.89)	(13.09 ± 0.68)	(13.05 ± 1.14)	(21.08 ± 3.37)
0.75	91.76 ± 0.01	92.05 ± 0.04	92.50 ± 0.04	92.71 ± 0.05	93.06 ± 0.01	93.56 ± 0.02	93.77 ± 0.03	93.95 ± 0.06
	(23.58 ± 1.05)	(17.30 ± 3.03)	(24.03 ± 3.00)	(24.22 ± 4.05)	(18.56 ± 0.63)	(19.44 ± 1.54)	(19.24 ± 2.84)	(25.87 ± 4.95)
L-Glutamic acid in an aqueous solution of tri-sodium citrate
0.1	91.83 ± 0.07	92.00 ± 0.04	92.14 ± 0.02	92.25 ± 0.01	92.36 ± 0.01	92.50 ± 0.05	92.59 ± 0.03	92.87 ± 0.03
	(23.01 ± 3.57)	(22.73 ± 2.30)	(14.79 ± 1.09)	(14.51 ± 0.75)	(14.67 ± 0.54)	(21.27 ± 2.74)	(23.33 ± 1.76)	(16.12 ± 1.57)
0.25	92.28 ± 0.03	92.44 ± 0.03	92.90 ± 0.03	93.01 ± 0.03	93.28 ± 0.03	93.50 ± 0.02	93.60 ± 0.07	93.70 ± 0.06
	(16.13 ± 1.84)	(13.40 ± 1.49)	(12.20 ± 1.89)	(15.75 ± 1.74)	(19.07 ± 1.39)	(16.54 ± 1.35)	(23.30 ± 3.89)	(23.59 ± 3.50)
0.50	93.16 ± 0.03	93.35 ± 0.03	93.74 ± 0.02	93.83 ± 0.04	94.18 ± 0.03	94.40 ± 0.03	94.54 ± 0.03	94.80 ± 0.02
	(25.23 ± 2.01)	(17.86 ± 1.69)	(13.98 ± 1.20)	(24.25 ± 2.27)	(16.30 ± 2.00)	(20.15 ± 1.60)	(27.98 ± 1.56)	(13.29 ± 1.05)
0.75	94.09 ± 0.01	94.23 ± 0.05	94.65 ± 0.01	94.74 ± 0.03	94.86 ± 0.05	95.17 ± 0.01	95.30 ± 0.03	95.51 ± 0.04
	(16.50 ± 0.48)	(17.87 ± 2.86)	(11.21 ± 0.60)	(15.94 ± 1.76)	(21.36 ± 2.53)	(14.19 ± 0.79)	(15.59 ± 1.39)	(21.00 ± 2.14)

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The V_2,ϕ⁰ values of both amino acids increase with an increase in the concentrations of the studied salts and also with an increase in temperature. As the V_2,ϕ⁰ values increase with an increase in molecular weight, the V_2,ϕ⁰ values are higher in GLU than ASP, because of the extra –CH₂ group. The V_2,ϕ⁰ values for both ASP and GLU are higher in aqueous solutions of TSC than in DST.

3.1.3. Apparent specific volume, v_ϕ. The apparent specific volume, v_ϕ, is calculated as follows

v_ϕ = V_2,ϕ/M. (3)

The apparent specific volume, v_ϕ, bears a relationship to taste quality in the order salty < sour < sweet < bitter and, probably, the entire range of human taste perception is confined to molecules with apparent specific volumes between 0.1 and 0.95 cm³ g⁻¹.³¹ The v_ϕ values for the studied systems are given in Table S2.† In water, the v_ϕ values for ASP and GLU fall within the sweet taste range³² (0.52–0.71 cm³ g⁻¹). ASP is sweeter than GLU in water. However, in aqueous solutions of DST and TSC, the v_ϕ values increase and, therefore, the sweetnesses of both ASP and GLU decrease as the m_B values increase.

3.1.4. Partial molar volumes of transfer, Δ_trV_2,ϕ⁰. The Δ_trV_2,ϕ⁰ values of the studied solutes, from water to aqueous solutions of DST and TSC, are calculated as follows:

Δ_trV_2,ϕ⁰ = V_2,ϕ⁰ (in aqueous solutions of DST/TSC) − V_2,ϕ⁰ (in water) (4)

The Δ_trV_2,ϕ⁰ values are positive for the studied amino acids and increase with the co-solute concentrations at all temperatures, as shown in Fig. 4(a, d, g and j). The Δ_trV_2,ϕ⁰ values of ASP and GLU decrease with temperature. The Δ_trV_2,ϕ⁰ values of both amino acids are greater in the case of TSC compared to DST, due to the high charge density.⁵ The magnitude of transfer is greater in the case of ASP compared to GLU.

Fig. 4 (a, d, g and j) Partial molar volume of transfer values, Δ_trV_2,ϕ⁰, of L-aspartic acid and L-glutamic acid vs. m_B for aqueous solutions of di-sodium tartrate and tri-sodium citrate at T = (◆) 288.15 K; (■) 293.15 K; (▲) 298.15 K; (×) 303.15 K; (*) 308.15 K; (●) 313.15 K; (+) 318.15 K; and (−) 323.15 K. (b, e, h and k) partial molar isentropic compression of transfer values, Δ_trK_s,_2,ϕ⁰, of L-aspartic acid and L-glutamic acid vs. m_B for aqueous solutions of di-sodium tartrate and tri-sodium citrate at T = (◆) 288.15 K; (■) 293.15 K; (▲) 298.15 K; (×) 303.15 K; (*) 308.15 K; (●) 313.15 K; (+) 318.15 K; and (−) 323.15 K. (c, f, i and l) Viscosity B-coefficient of transfer values, Δ_trB, of L-aspartic acid and L-glutamic acid vs. m_B for aqueous solutions of di-sodium tartrate and tri-sodium citrate at T = (◆) 288.15 K; (■) 298.15 K; (▲) 308.15 K; and (×) 308.15 K.

The magnitude of Δ_trV_2,ϕ⁰ initially increases sharply, and the increase is less at higher co-solute concentrations. A co-sphere overlap model³³ is used to interpret these results. According to this model, hydrophilic (the –NH₂ and –COOH parts of the solute)-ionic (the Na⁺ and ⁻COO⁻ parts of the co-solute) and hydrophilic (the –NH₂ and –COOH groups of the solute)-hydrophilic (the –OH groups of the co-solute) interactions contribute positively, and hydrophobic (the alkyl groups of the solute)-hydrophilic (the –OH groups of the co-solute) and hydrophobic (the alkyl groups of the solute)-ionic (the Na⁺ and ⁻COO⁻ parts of the co-solute) interactions contribute negatively to the Δ_trV_2,ϕ⁰ values. Therefore, in the present system, the positive Δ_trV_2,ϕ⁰ values for these amino acids over the co-solute concentration range studied suggest that hydrophilic–ionic and hydrophilic–hydrophilic interactions dominate over hydrophobic–hydrophilic and hydrophobic–ionic interactions. Furthermore, the decrease in the magnitude of Δ_trV_2,ϕ⁰ from ASP to GLU indicates the building up of hydrophobic–ionic interactions due to the extra –CH₂ group. The additional –CH₂ group exerts a destructive effect on the polar and charged group hydration spheres of the amino acids. The low Δ_trV_2,ϕ⁰ values for GLU are in line with the observation that Δ_trV_2,ϕ⁰ values decrease with an increase in the lengths of the alkyl side chains of amino acids.¹⁸

3.1.5. Hydration number, N_h. The hydration number, N_h of the amino acids in water and in aqueous DST/TSC solutions can be calculated by using the following equation.³⁴

N_h (in water) = V_elect/(V⁰_e−V⁰_b) (5)

In the above equation, V⁰_e = molar volume of electrostricted water and V⁰_b = molar volume of bulk water/solvent. The (V⁰_e − V⁰_b) values are approximately −2.9 cm³ mol⁻¹ at 288.15 K, −3.3 cm³ mol⁻¹ at 298.15 K and −4.0 cm³ mol⁻¹ at 308.15 K.³⁵ The V_elect values have been calculated from the corresponding V_2,ϕ⁰ values using the equation:

V_elect = V_2,ϕ⁰ − V⁰_int (6)

where the intrinsic molar volume, V⁰_int, can be estimated from the crystallographic volume, V_cryst as follows:³⁶

V⁰_int = (0.7/0.634)V_cryst. (7)

The N_h data in Table S3† indicate that the dehydration of ASP and GLU increases with the co-solute molality. The N_h values for ASP are higher than for GLU and, also, the decreases in the N_h values with m_B are larger in the case of ASP compared to GLU. TSC is found to be an effective preservative for dehydration processes, therefore, its use in the food industry is more preferred than DST.³⁷ TSC has also been found to be a better food emulsifier than DST in the literature.⁵ TSC helps control the stickiness of some doughs through removing extra water and creating a firmer texture. Thus, it helps in the processing of baked foods.^38,39 Therefore, the N_h data also indicate that TSC is a better food preservative than DST.

3.1.6. Partial molar expansion, E_2,ϕ⁰. To discuss the effects of temperature on the V_2,ϕ⁰ values, the partial molar expansion values, E_2,ϕ⁰ (E_2,ϕ⁰ = (∂V_2,ϕ⁰/∂T)_P), along with the 2^nd order derivatives, (∂²V_2,ϕ⁰/∂T²)_P, have been calculated by the method of least-squares using the following equation:

V_2,ϕ⁰ = a + bT + cT² (8)

where a, b and c are constants, and T is the temperature in Kelvin. The (∂V_2,ϕ⁰/∂T)_P values are positive for the studied solutes (Table S4†), except for ASP in TSC at m_B = 0.75 mol kg⁻¹ and at T = 323.15 K. The (∂V_2,ϕ⁰/∂T)_P values decrease with temperature, except for GLU in DST at m_B = 0.25 mol kg⁻¹ at higher temperatures and GLU in TSC at m_B = 0.1 mol kg⁻¹ at all temperatures. However, the (∂V_2,ϕ⁰/∂T)_P values do not follow any regular trend in relation to the m_B values.

Hepler⁴⁰ used a general thermodynamic equation, {(∂C_P,2⁰/∂P)_T = −T(∂²V_2,ϕ⁰/∂T²)_P}, to determine the capacity of a solute to act as a structure-maker or a structure-breaker in solution. If the term (∂²V_2,ϕ⁰/∂T²)_P < 0, the solute is a structure-breaker and if (∂²V_2,ϕ⁰/∂T²)_P > 0, the solute is a structure-maker. The negative values of (∂²V_2,ϕ⁰/∂T²)_P in aqueous solutions of the co-solutes suggest that ASP and GLU act as structure-breaking solutes. However, at m_B = 0.1 mol kg⁻¹, GLU acts as a structure-maker in the case of TSC.

3.1.7. Interaction coefficients. Interaction coefficients have been calculated using the McMillan–Mayer equation⁴¹ from the transfer volume, Δ_trV_2,ϕ⁰, data for the studied solutes as follows:

Δ_trV_2,ϕ⁰ = 2V_AB·m_B + 3V_ABB·m_B² + … (9)

where A stands for the solute and B for the co-solute, and V_AB and V_ABB are the volumetric pair and triplet interaction coefficients, respectively (Table S5†). The higher magnitudes of V_AB (positive values) in comparison to V_ABB (negative values, except for GLU in DST at T = 323.15 K) for the studied solutes at all temperatures suggest the predominance of pair-wise interactions. This suggests the dominance of hydrophilic–ionic/hydrophilic interactions, which again strengthens the above-mentioned views.

3.2. Acoustic measurements

3.2.1. Speed of sound, u. The speed of sound, u, of amino acids (ASP and GLU) in water and in aqueous solutions of DST and TSC at m_B = 0.10, 0.25, 0.50 and 0.75 mol kg⁻¹ and at temperatures from 288.15 to 323.15 K are given in Table 4. The u values of water are in agreement with the literature values.⁴² The u values in aqueous solutions of DST and TSC match well with the available literature data,^16–21,23 as seen in Fig. 5. The u values of ASP and GLU in water are in close agreement with the available literature data, as seen in Fig. 6.^25–27 The u values increase with the m_A, m_B and T values, as is evident from the 3-D plot (Fig. 3(c)) of u versus m_A for ASP at different temperatures in TSC at m_B = 0.1 mol kg⁻¹.

Fig. 5 (a) Plots of speed of sound values, u, versus molality, m_B, for aqueous solutions of TSC and comparisons with the literature values at different temperatures. (b) Plots of speed of sound values, u, versus molality, m_B, for aqueous solutions of DST and comparisons with the literature values at different temperatures.

Fig. 6 (a) Plots of speed of sound values, u, versus molality, m_A, for aqueous solutions of ASP and comparisons with the literature values at different temperatures. (b) Plots of speed of sound values, u, versus molality, m_A, for aqueous solutions of GLU and comparisons with the literature values at different temperatures.

Table 4 The speed of sound values, u, of L-aspartic acid and L-glutamic acid in water and in aqueous solutions of di-sodium tartrate and tri-sodium citrate at T values from 288.15 to 323.15 K and P = 101.3 kPa

m A/mol kg^−1	u/m sec^−1
	288.15 K	293.15 K	298.15 K	303.15 K	308.15 K	313.15 K	318.15 K	323.15 K
m A is the molality of the solute in water or water + DST/TSC. mB is the molality of DST/TSC in water. Standard uncertainties, u, are u(T) = 0.03 K, u(P) = 0.5 kPa, u(m) = 2.8 × 10^−4 mol kg^−1, u(u) = 0.6 m s^−1.
L-Aspartic acid in water
0.00000	1466.83	1483.03	1497.10	1510.02	1519.83	1529.98	1536.40	1542.99
0.00517	1467.53	1483.68	1497.71	1510.59	1520.34	1530.45	1536.84	1543.38
0.00712	1467.78	1483.92	1497.94	1510.81	1520.54	1530.62	1536.99	1543.52
0.00921	1468.04	1484.17	1498.18	1511.04	1520.75	1530.80	1537.15	1543.67
0.01109	1468.28	1484.39	1498.40	1511.25	1520.94	1530.96	1537.30	1543.80
0.01300	1468.51	1484.62	1498.62	1511.46	1521.13	1531.12	1537.45	1543.94
0.01506	1468.76	1484.86	1498.85	1511.68	1521.33	1531.29	1537.60	1544.08
L-Aspartic acid in an aqueous solution of di-sodium tartrate at m B = 0.1 mol kg ^−1
0.00000	1478.73	1494.57	1511.87	1522.45	1534.08	1543.75	1550.05	1557.45
0.00502	1479.25	1495.10	1512.40	1522.98	1534.59	1544.18	1550.48	1557.85
0.00741	1479.50	1495.34	1512.65	1523.23	1534.83	1544.38	1550.68	1558.04
0.01180	1479.95	1495.80	1513.28	1523.69	1535.27	1544.75	1551.05	1558.39
0.01306	1480.07	1495.93	1513.34	1523.82	1535.39	1544.85	1551.16	1558.48
0.01732	1480.51	1496.36	1514.04	1524.26	1535.81	1545.21	1551.51	1558.82
L-Aspartic acid in an aqueous solution of di-sodium tartrate at m B = 0.25 mol kg ^−1
0.00000	1504.97	1519.22	1533.45	1544.85	1554.33	1561.75	1569.19	1577.89
0.00584	1505.61	1519.86	1534.09	1545.48	1554.91	1562.23	1569.64	1578.31
0.00817	1505.86	1520.11	1534.34	1545.73	1555.14	1562.42	1569.82	1578.47
0.01106	1506.17	1520.43	1534.65	1546.04	1555.42	1562.65	1570.03	1578.67
0.01337	1506.42	1520.67	1534.90	1546.28	1555.64	1562.83	1570.20	1578.82
0.01555	1506.65	1520.91	1535.13	1546.51	1555.85	1563.00	1570.36	1578.97
0.01667	1506.77	1521.03	1535.25	1546.63	1555.95	1563.08	1570.43	1579.04
L-Aspartic acid in an aqueous solution of di-sodium tartrate at m B = 0.50 mol kg ^−1
0.00000	1549.36	1558.64	1569.41	1579.85	1588.09	1595.45	1601.10	1609.00
0.00638	1550.10	1559.37	1570.12	1580.54	1588.70	1595.96	1601.62	1609.47
0.00782	1550.27	1559.53	1570.28	1580.69	1588.84	1596.07	1601.74	1609.57
0.00982	1550.50	1559.76	1570.50	1580.89	1589.02	1596.22	1601.90	1609.72
0.01307	1550.87	1560.12	1570.85	1581.23	1589.33	1596.47	1602.16	1609.95
0.01509	1551.10	1560.35	1571.07	1581.44	1589.52	1596.62	1602.31	1610.09
0.01639	1551.24	1560.49	1571.20	1581.57	1589.63	1596.72	1602.41	1610.18
L-Aspartic acid in an aqueous solution of di-sodium tartrate at m B = 0.75 mol kg ^−1
0.00000	1588.75	1597.00	1605.38	1615.75	1621.84	1628.04	1633.00	1641.75
0.00547	1589.45	1597.68	1606.03	1616.37	1622.42	1628.51	1633.50	1642.22
0.00739	1589.69	1597.92	1606.26	1616.58	1622.62	1628.67	1633.67	1642.38
0.01025	1590.05	1598.27	1606.59	1616.90	1622.91	1628.90	1633.92	1642.62
0.01347	1590.45	1598.66	1606.97	1617.25	1623.26	1629.16	1634.20	1642.89
0.01664	1590.84	1599.04	1607.33	1617.60	1623.57	1629.41	1634.48	1643.15
L-Aspartic acid in an aqueous solution of tri-sodium citrate at m B = 0.1 mol kg ^−1
0.00000	1487.73	1503.57	1517.21	1529.07	1539.24	1548.45	1555.13	1562.78
0.00576	1488.28	1504.12	1517.76	1529.62	1539.76	1548.87	1555.53	1563.15
0.00754	1488.45	1504.29	1517.93	1529.79	1539.91	1549.00	1555.65	1563.27
0.01002	1488.69	1504.52	1518.16	1530.02	1540.13	1549.18	1555.82	1563.42
0.01189	1488.86	1504.70	1518.34	1530.19	1540.30	1549.31	1555.94	1563.54
0.0152	1489.17	1505.01	1518.65	1530.49	1540.59	1549.55	1556.16	1563.75
L-Aspartic acid in an aqueous solution of tri-sodium citrate at m B = 0.25 mol kg ^−1
0.00000	1517.97	1533.22	1545.99	1557.02	1566.44	1574.85	1580.99	1587.00
0.00624	1518.60	1533.83	1546.57	1557.57	1566.95	1575.25	1581.36	1587.34
0.00784	1518.76	1533.98	1546.71	1557.71	1567.08	1575.35	1581.45	1587.42
0.01080	1519.05	1534.27	1546.98	1557.97	1567.31	1575.53	1581.62	1587.58
0.01208	1519.18	1534.39	1547.10	1558.08	1567.41	1575.61	1581.69	1587.65
0.01490	1519.46	1534.66	1547.35	1558.32	1567.63	1575.78	1581.85	1587.79
0.01825	1519.79	1534.97	1547.65	1558.61	1567.90	1575.99	1582.03	1587.96
L-Aspartic acid in an aqueous solution of tri-sodium citrate at m B = 0.50 mol kg ^−1
0.00000	1568.36	1582.64	1593.94	1603.61	1611.76	1618.75	1624.10	1630.01
0.00597	1569.02	1583.27	1594.55	1604.20	1612.28	1619.16	1624.48	1630.34
0.00809	1569.26	1583.49	1594.77	1604.40	1612.46	1619.30	1624.61	1630.46
0.00985	1569.45	1583.67	1594.95	1604.57	1612.61	1619.42	1624.72	1630.56
0.01284	1569.77	1583.98	1595.26	1604.86	1612.85	1619.62	1624.91	1630.73
0.01520	1570.03	1584.22	1595.50	1605.08	1613.05	1619.77	1625.05	1630.86
0.0181	1570.34	1584.46	1595.78	1605.35	1613.28	1619.95	1625.22	1631.03
L-Aspartic acid in an aqueous solution of tri-sodium citrate at m B = 0.75 mol kg ^−1
0.00000	1618.75	1632.06	1641.90	1650.20	1657.08	1662.45	1667.20	1673.45
0.00626	1619.55	1632.82	1642.62	1650.89	1657.68	1662.89	1667.60	1673.84
0.00788	1619.75	1633.01	1642.80	1651.06	1657.83	1663.00	1667.70	1673.94
0.01082	1620.12	1633.36	1643.13	1651.38	1658.10	1663.21	1667.89	1674.13
0.01180	1620.24	1633.47	1643.24	1651.48	1658.18	1663.28	1667.95	1674.19
0.01461	1620.59	1633.80	1643.55	1651.77	1658.44	1663.48	1668.13	1674.36
0.01732	1620.92	1634.12	1643.85	1652.05	1658.68	1663.67	1668.30	1674.53
L-Glutamic acid in water
0.01104	1467.12	1483.26	1497.44	1510.18	1520.06	1530.36	1536.68	1543.40
0.01308	1467.16	1483.31	1497.49	1510.23	1520.12	1530.42	1536.73	1543.45
0.01522	1467.21	1483.36	1497.54	1510.28	1520.17	1530.47	1536.79	1543.51
0.02078	1467.34	1483.49	1497.68	1510.43	1520.32	1530.62	1536.94	1543.66
0.02517	1467.45	1483.60	1497.79	1510.54	1520.44	1530.74	1537.06	1543.79
0.03030	1467.57	1483.72	1497.92	1510.68	1520.57	1530.88	1537.21	1543.93
L-Glutamic acid in an aqueous solution of di-sodium tartrate at m B = 0.1 mol kg ^−1
0.01288	1479.08	1494.93	1512.24	1522.82	1534.46	1544.13	1550.43	1557.83
0.01523	1479.15	1495.00	1512.31	1522.89	1534.53	1544.20	1550.50	1557.91
0.01930	1479.27	1495.11	1512.43	1523.01	1534.65	1544.32	1550.63	1558.03
0.02496	1479.43	1495.28	1512.59	1523.18	1534.82	1544.49	1550.80	1558.20
0.03127	1479.61	1495.46	1512.78	1523.37	1535.01	1544.68	1550.99	1558.40
0.03591	1479.74	1495.60	1512.92	1523.52	1535.16	1544.82	1551.14	1558.55
L-Glutamic acid in an aqueous solution of di-sodium tartrate at m B = 0.25 mol kg ^−1
0.01410	1505.42	1519.67	1533.90	1545.31	1554.79	1562.22	1569.66	1578.36
0.01930	1505.89	1520.15	1534.39	1545.80	1555.29	1562.71	1570.16	1578.86
0.02391	1506.10	1520.36	1534.60	1546.01	1555.50	1562.92	1570.37	1579.07
0.03000	1506.41	1520.67	1534.92	1546.33	1555.82	1563.25	1570.69	1579.40
0.03535	1506.52	1520.79	1535.03	1546.45	1555.94	1563.37	1570.82	1579.52
L-Glutamic acid in an aqueous solution of di-sodium tartrate at m B = 0.50 mol kg ^−1
0.01104	1549.82	1559.11	1569.89	1580.33	1588.57	1595.94	1601.59	1609.49
0.01239	1549.87	1559.16	1569.94	1580.38	1588.62	1595.99	1601.64	1609.54
0.01547	1549.99	1559.28	1570.05	1580.50	1588.74	1596.11	1601.76	1609.67
0.02012	1550.13	1559.42	1570.20	1580.64	1588.89	1596.26	1601.91	1609.82
0.02521	1550.34	1559.64	1570.42	1580.87	1589.12	1596.49	1602.14	1610.05
0.03006	1550.78	1560.09	1570.86	1581.32	1589.57	1596.95	1602.60	1610.51
L-Glutamic acid in an aqueous solution of di-sodium tartrate at m B = 0.75 mol kg ^−1
0.01159	1589.26	1597.51	1605.79	1616.32	1622.37	1628.57	1633.54	1642.29
0.01375	1589.35	1597.60	1605.89	1616.42	1622.47	1628.67	1633.64	1642.39
0.01765	1589.52	1597.78	1606.07	1616.60	1622.64	1628.86	1633.82	1642.58
0.01995	1589.63	1597.88	1606.17	1616.71	1622.75	1628.97	1633.93	1642.69
0.02676	1589.93	1598.18	1606.49	1617.02	1623.07	1629.29	1634.25	1643.01
L-Glutamic acid in an aqueous solution of tri-sodium citrate at m B = 0.1 mol kg ^−1
0.01247	1488.11	1503.95	1517.59	1529.46	1539.63	1548.84	1555.52	1563.17
0.01463	1488.18	1504.02	1517.66	1529.52	1539.67	1548.91	1555.59	1563.23
0.01634	1488.23	1504.07	1517.72	1529.58	1539.75	1548.97	1555.65	1563.29
0.02218	1488.41	1504.26	1517.90	1529.76	1539.94	1549.16	1555.84	1563.47
0.02857	1488.62	1504.47	1518.11	1529.97	1540.14	1549.36	1556.05	1563.67
0.03390	1488.79	1504.64	1518.28	1530.14	1540.32	1549.54	1556.22	1563.84
L-Glutamic acid in an aqueous solution of tri-sodium citrate at mB= 0.25 mol kg^−1
0.01213	1518.40	1533.65	1546.43	1557.46	1566.88	1575.30	1581.44	1587.45
0.01438	1518.48	1533.73	1546.52	1557.55	1566.97	1575.39	1581.53	1587.54
0.01771	1518.60	1533.86	1546.64	1557.67	1567.10	1575.51	1581.66	1587.66
0.02308	1518.79	1534.05	1546.84	1557.87	1567.31	1575.72	1581.86	1587.87
0.02531	1518.88	1534.13	1546.92	1557.96	1567.39	1575.80	1581.95	1587.96
0.03401	1519.19	1534.45	1547.24	1558.29	1567.73	1576.14	1582.28	1588.29
L-Glutamic acid in an aqueous solution of tri-sodium citrate at mB= 0.50 mol kg^−1
0.01104	1568.85	1583.14	1594.44	1604.12	1612.26	1619.26	1624.61	1630.52
0.01239	1568.92	1583.20	1594.51	1604.18	1612.33	1619.32	1624.67	1630.58
0.01547	1569.06	1583.34	1594.65	1604.32	1612.47	1619.47	1624.82	1630.72
0.02012	1569.27	1583.55	1594.86	1604.54	1612.69	1619.69	1625.04	1630.94
0.02521	1569.51	1583.79	1595.10	1604.78	1612.93	1619.93	1625.28	1631.17
0.03006	1569.73	1583.96	1595.33	1605.02	1613.16	1620.16	1625.52	1631.40
L-Glutamic acid in an aqueous solution of tri-sodium citrate at mB= 0.75 mol kg^−1
0.01088	1619.34	1632.66	1642.51	1650.81	1657.69	1663.06	1667.81	1674.06
0.01408	1619.52	1632.83	1642.69	1650.99	1657.87	1663.24	1667.99	1674.24
0.01532	1619.59	1632.90	1642.75	1651.06	1657.94	1663.31	1668.06	1674.31
0.02000	1619.85	1633.17	1643.02	1651.32	1658.21	1663.57	1668.32	1674.58
0.02799	1620.29	1633.61	1643.47	1651.78	1658.66	1664.03	1668.77	1675.03
0.03107	1620.47	1633.79	1643.64	1651.95	1658.84	1664.20	1668.95	1675.21

---

3.2.2. Apparent molar isentropic compression, K_s,2,ϕ. The K_s,2,ϕ values for solutes in water and in aqueous solutions of DST and TSC at m_B = 0.10, 0.25, 0.50, and 0.75 mol kg⁻¹ and at temperatures from 288.15 to 323.15 K (given in Table S6†) have been calculated using the following relationship:

K_s,2,ϕ = (κ_sM/ρ) − {(κ_s^oρ − κ_sρ₀)/(m_Aρρ₀)} (10)

The K_s,2,ϕ values are negative, and their magnitudes decrease with increases in the temperature and in the concentrations of both the solute and co-solute. ρ and ρ₀, and κ_s and κ_s^o are the densities and isentropic compressibilities of the solution and solvent, respectively. The isentropic compressibilities (κ_s) were calculated from the measured speed of sound (u) as follows:

κ_s = 1/u²ρ. (11)

3.2.3. Partial molar isentropic compression, K_s,2,ϕ⁰. The K_s,2,ϕ⁰ values have been calculated using the least squares fitting of the respective data to the given equation:

K_s,2,ϕ = K_s,2,ϕ⁰ + S_km. (12)

At infinite dilution, K_s,2,ϕ⁰, the apparent molar isentropic compression, and the partial molar isentropic compression, K_s,2⁰, become the same. The K_s,2,ϕ⁰ values of the studied solutes in water agree well with the literature values.^{25–27,29,30} The K_s,2,ϕ⁰ values of the solutes are negative in water as well as in aqueous solutions of the co-solutes, which may be due to the hydration of the solutes, as the hydrated water molecules are already compressed and are thus less compressible than those present in the bulk. The magnitudes of the K_s,2,ϕ⁰ values decrease with temperature and with the co-solute concentrations (Table 5).

Table 5 Partial molar isentropic compression values, K_s,2,ϕ⁰, of L-aspartic acid and L-glutamic acid in water and in aqueous solutions of di-sodium tartrate and tri-sodium citrate at T values from 288.15 to 323.15 K and P = 101.3 kPa

m B/mol kg^−1	10^14·Ks,2,ϕ^0/m^3 mol^−1 Pa^−1
	288.15 K	293.15 K	298.15 K	303.15 K	308.15 K	313.15 K	318.15 K	323.15 K
a Ref. 25. b Ref. 26. c Ref. 27. d Ref. 29. e Ref. 30; parentheses contain Sk (m^3 mol^−2 kg Pa^−1) values; standard uncertainties, u, are u(T) = 0.03 K, u(P) = 0.5 kPa, u(m) = 2.8 × 10^−4 mol kg^−1.
L-Aspartic acid in an aqueous solution of di-sodium tartrate
0	−7.51 ± 0.01	−7.09 ± 0.02	−6.63 ± 0.01	−6.26 ± 0.01	−5.60 ± 0.84	−4.50 ± 0.01	−4.11 ± 0.02	−3.64 ± 0.01
	(11.45 ± 0.80)	(16.68 ± 1.44)	−3.61^a, −6.67^b, −7.14^c	(18.28 ± 0.88)	−3.06 ^a	(12.76 ± 0.52)	(17.70 ± 2.30)	(13.34 ± 0.63)
			(17.12 ± 0.28)	−6.24^b^,^c	(19.59 ± 0.84)	−4.53^b^,^c
					−5.60^b, −5.61^c
0.1	−5.39 ± 0.01	−5.29 ± 0.01	−5.19 ± 0.02	−5.08 ± 0.01	−4.75 ± 0.01	−3.86 ± 0.01	−3.81 ± 0.01	−3.50 ± 0.01
	(7.39 ± 0.89)	(7.88 ± 0.50)	(7.62 ± 1.33)	(6.25 ± 0.35)	(7.20 ± 0.75)	(8.42 ± 0.95)	(7.48 ± 0.56)	(8.02 ± 0.98)
0.25	−5.09 ± 0.01	−4.94 ± 0.01	−4.82 ± 0.01	−4.63 ± 0.01	−4.18 ± 0.01	−3.23 ± 0.02	2.96 ± 0.01	−2.63 ± 0.01
	(11.00 ± 0.42)	(8.48 ± 0.57)	(10.92 ± 0.44)	(8.86 ± 0.84)	(13.29 ± 0.45)	(11.71 ± 1.23)	(12.61 ± 0.69)	(12.95 ± 0.88)
0.50	−4.40 ± 0.01	−4.27 ± 0.01	−4.05 ± 0.01	−3.82 ± 0.01	−3.23 ± 0.01	−2.50 ± 0.01	−2.56 ± 0.01	−2.19 ± 0.01
	(8.57 ± 0.66)	(10.48 ± 1.03)	(10.40 ± 1.22)	(13.37 ± 0.64)	(8.73 ± 0.86)	(12.56 ± 1.16)	(9.18 ± 0.56)	(9.62 ± 0.58)
0.75	−4.10 ± 0.01	−3.88 ± 0.01	−3.60 ± 0.01	−3.34 ± 0.01	−3.01 ± 0.01	−2.18 ± 0.01	−2.39 ± 0.01	−2.16 ± 0.01
	(9.10 ± 0.50)	(7.71 ± 0.36)	(7.67 ± 0.74)	(9.43 ± 0.55)	(8.06 ± 0.33)	(10.92 ± 0.25)	(10.13 ± 0.81)	(8.75 ± 0.43)
L-Aspartic acid in an aqueous solution of tri-sodium citrate
0.1	−4.66 ± 0.01	−4.50 ± 0.01	4.37 ± 0.01	−4.29 ± 0.01	−3.89 ± 0.01	−2.99 ± 0.01	−2.77 ± 0.01	−2.47 ± 0.01
	(8.65 ± 0.43)	(7.58 ± 1.05)	(8.51 ± 0.54)	(12.76 ± 0.81)	(9.43 ± 0.61)	(9.30 ± 0.98)	(11.02 ± 1.23)	(7.58 ± 1.05)
0.25	−4.20 ± 0.01	−3.89 ± 0.01	−3.56 ± 0.01	−3.30 ± 0.01	−2.89 ± 0.01	−2.01 ± 0.01	−1.79 ± 0.02	−1.54 ± 0.01
	(8.33 ± 1.12)	(7.91 ± 0.96)	(9.29 ± 0.72)	(8.03 ± 0.55)	(8.54 ± 0.62)	(9.38 ± 0.80)	(10.16 ± 1.24)	(8.07 ± 0.52)
0.50	−3.61 ± 0.01	−3.27 ± 0.01	−3.04 ± 0.02	−2.87 ± 0.02	−2.39 ± 0.02	−1.59 ± 0.02	−1.40 ± 0.02	−1.04 ± 0.01
	(9.93 ± 0.74)	(10.41 ± 0.81)	(2.97 ± 1.65)	(10.01 ± 1.44)	(13.60 ± 1.70)	(8.54 ± 1.65)	(8.33 ± 1.46)	(1.07 ± 0.37)
0.75	−3.31 ± 0.01	−3.01 ± 0.01	−2.74 ± 0.01	−2.50 ± 0.01	−2.01 ± 0.01	−1.10 ± 0.01	−0.88 ± 0.01	−0.84 ± 0.01
	(9.49 ± 0.62)	(9.41 ± 0.30)	(9.33 ± 0.69)	(8.00 ± 0.59)	(10.11 ± 1.13)	(0.61 ± 0.39)	(11.17 ± 0.72)	(1.11 ± 0.37)
10 ^16 ·K s,2,ϕ ^0 /m ^3 mol ^−1 Pa ^−1
L-Glutamic acid in an aqueous solution of di-sodium tartrate
0	−3.86 ± 0.01	−3.50 ± 0.01	−3.18 ± 0.01	−2.75 ± 0.02	−2.46 ± 0.01	−2.18 ± 0.01	−2.06 ± 0.02	−1.92 ± 0.01
	−3.37^a	(5.81 ± 0.60)	−3.20^a, −3.18^d, −3.92^e	(5.79 ± 1.08)	−2.20^a	(6.80 ± 0.54)	(6.58 ± 0.89)	(8.64 ± 0.61)
	(5.87 ± 0.67)		(6.25 ± 0.56)		(7.16 ± 0.68)
0.1	−2.58 ± 0.02	−2.44 ± 0.01	−2.30 ± 0.01	−2.16 ± 0.01	−2.03 ± 0.01	−1.85 ± 0.01	−1.80 ± 0.02	−1.71 ± 0.01
	(4.57 ± 0.63)	(4.63 ± 0.44)	(4.42 ± 0.59)	(4.91 ± 0.26)	(5.26 ± 0.52)	(4.91 ± 0.33)	(4.81 ± 0.67)	(5.47 ± 0.44)
0.25	−2.45 ± 0.01	−2.34 ± 0.01	−2.13 ± 0.01	−2.02 ± 0.01	−1.94 ± 0.01	−1.80 ± 0.01	−1.72 ± 0.01	−1.60 ± 0.01
	(4.13 ± 0.20)	(4.10 ± 0.53)	(4.86 ± 0.47)	(3.95 ± 0.28)	(4.30 ± 0.54)	(6.42 ± 0.53)	(4.91 ± 0.46)	(4.51 ± 0.36)
0.50	−2.33 ± 0.02	−2.23 ± 0.01	−2.07 ± 0.02	−1.93 ± 0.03	−1.75 ± 0.02	−1.63 ± 0.02	−1.57 ± 0.03	−1.46 ± 0.01
	(4.55 ± 0.93)	(4.83 ± 0.61)	(5.03 ± 0.74)	(5.28 ± 1.13)	(4.76 ± 0.80)	(5.48 ± 0.73)	(4.85 ± 1.26)	(5.25 ± 0.60)
0.75	−2.28 ± 0.02	−2.16 ± 0.02	−2.00 ± 0.01	−1.87 ± 0.02	−1.73 ± 0.02	−1.58 ± 0.02	−1.47 ± 0.02	−1.40 ± 0.01
	(6.44 ± 1.12)	(6.33 ± 0.81)	(5.86 ± 0.44)	(6.13 ± 1.23)	(6.46 ± 1.04)	(7.82 ± 1.12)	(6.15 ± 1.23)	(6.94 ± 0.58)
L-Glutamic acid in an aqueous solution of tri-sodium citrate
0.1	−2.19 ± 0.02	−2.04 ± 0.02	−1.94 ± 0.02	−1.77 ± 0.02	−1.69 ± 0.01	−1.47 ± 0.02	−1.43 ± 0.01	−1.33 ± 0.02
	(5.49 ± 0.67)	(4.35 ± 0.71)	(5.21 ± 0.96)	(5.62 ± 0.74)	(5.27 ± 0.59)	(4.55 ± 0.66)	(5.82 ± 0.61)	(5.91 ± 0.80)
0.25	−2.05 ± 0.02	−1.90 ± 0.02	−1.77 ± 0.01	−1.62 ± 0.02	−1.49 ± 0.02	−1.31 ± 0.02	−1.27 ± 0.02	−1.15 ± 0.01
	(5.71 ± 0.68)	(6.24 ± 1.06)	(4.68 ± 0.56)	(6.34 ± 0.87)	(4.84 ± 0.91)	(6.43 ± 0.91)	(6.40 ± 0.87)	(4.43 ± 0.62)
0.50	−1.90 ± 0.01	−1.77 ± 0.01	−1.60 ± 0.02	−1.46 ± 0.01	−1.35 ± 0.01	−1.23 ± 0.02	−1.08 ± 0.01	−1.03 ± 0.01
	(4.97 ± 0.71)	(6.04 ± 0.54)	(6.09 ± 0.83)	(6.47 ± 0.56)	(5.19 ± 0.66)	(3.18 ± 1.05)	(1.61 ± 0.43)	(1.04 ± 0.16)
0.75	−1.76 ± 0.02	−1.65 ± 0.01	−1.49 ± 0.01	−1.36 ± 0.01	−1.23 ± 0.02	−1.07 ± 0.01	−1.01 ± 0.01	−1.00 ± 0.01
	(5.66 ± 0.89)	(5.70 ± 0.67)	(6.84 ± 0.68)	(5.43 ± 0.60)	(4.89 ± 0.81)	(0.59 ± 0.12)	(0.15 ± 0.01)	(0.45 ± 0.22)

---

3.2.4. Partial molar isentropic compression of transfer, Δ_trK_s,2,ϕ⁰. The partial molar isentropic compression of transfer values (Δ_trK_s,2,ϕ⁰) were calculated using the following equation:

Δ_trK_s,2,ϕ⁰ = K_s,2,ϕ⁰ (in aqueous solutions of DST/TSC) − K_s,2,ϕ⁰ (in water). (13)

The Δ_trK_s,2,ϕ⁰ values are positive for all solutes; this suggests the predominance of hydrophilic–ionic/hydrophilic interactions and the strengthening of these interactions over the entire studied concentration range. The magnitudes decrease with an increase in temperature, as shown in Fig. 4(b, e, h and k). Due to interactions between the hydrophilic sites of the amino acids and the citrate and tartrate ions of the co-solutes, the less compressible water molecules in the hydration shells of the solute molecules come out in the bulk water, hence exhibiting positive Δ_trK_s,2,ϕ⁰ values. Higher Δ_trK_s,2,ϕ⁰ values are observed for the studied solutes in the case of TSC compared to DST.

3.3. Viscosity measurements

Viscosities have been determined for ASP and GLU in water and in aqueous solutions of DST and TSC, over an m_B value range from 0.1–0.75 mol kg⁻¹ and from T = 288.15 to 318.15 K, from flow time measurements using the following expression:

η/ρ = At − B/t (14)

where ρ is the density of the solution, t is the flow time, and A and B are viscometric constants (A = 0.0000669 mPa m³ kg⁻¹ and B = 0.2244 mPa m³ s² kg⁻¹). The η values of TSC and GLU in water at 298.15 K matched well with the literature data (Fig. S1, ESI†).^22,28 The η values increase with an increase in the concentration of amino acid in water and in aqueous solutions of DST/TSC, and decrease with temperature (Table 6). The variation in η values for solutions of GLU in aqueous DST at different temperatures are shown in Fig. 3(d) (viscosity, η, versus molality, m_A, for GLU in DST at m_B = 0.1 mol kg⁻¹ as a function of temperature).

Table 6 Viscosities, η, of L-aspartic acid and L-glutamic acid in water and in aqueous solutions of di-sodium tartrate and tri-sodium citrate at T values from 288.15 to 318.15 K and P = 101.3 kPa

η/mPa s
m A	T/K	T/K	T/K	T/K
mol kg^−1	288.15	298.15	308.15	318.15
m A is the molality of the solute in water or water + DST/TSC (solvent). mB is the molality of DST/TSC in water. Standard uncertainties are u(T) = 0.03 K, u(P) = 0.5 kPa, u(m) = 2.8 × 10^−4 mol kg^−1 and u(η) = 0.012 mPa s.
L-Aspartic acid in water
	η 0 = 1.1382 mPa s	η 0 = 0.8904 mPa s	η 0 = 0.7194 mPa s	η 0 = 0.5963 mPa s
0.00517	1.1390	0.8910	0.7197	0.5967
0.00712	1.1392	0.8912	0.7200	0.5968
0.00921	1.1395	0.8915	0.7202	0.5970
0.01109	1.1397	0.8917	0.7205	0.5972
0.01300	1.1400	0.8919	0.7206	0.5973
0.01506	1.1404	0.8921	0.7208	0.5975
L-Aspartic acid in an aqueous solution of di-sodium tartrate at mB= 0.10 mol kg^−1
	η 0 = 1.1631 mPa s	η 0 = 0.9518 mPa s	η 0 = 0.7783 mPa s	η 0 = 0.6644 mPa s
0.00502	1.1637	0.9525	0.7787	0.6647
0.00741	1.1640	0.9528	0.7790	0.6650
0.01180	1.1643	0.9529	0.7792	0.6651
0.01306	1.1646	0.9531	0.7794	0.6653
0.01732	1.1651	0.9534	0.7797	0.6655
L-Aspartic acid in an aqueous solution of di-sodium tartrate at mB= 0.25 mol kg^−1
	η 0 = 1.2425 mPa s	η 0 = 1.0248 mPa s	η 0 = 0.8544 mPa s	η 0 = 0.7244 mPa s
0.00584	1.2434	1.0255	0.8550	0.7247
0.00817	1.2436	1.0257	0.8553	0.7250
0.01106	1.2439	1.0260	0.8555	0.7253
0.01337	1.2442	1.0264	0.8556	0.7255
0.01555	1.2446	1.0266	0.8559	0.7256
0.01667	1.2451	1.0269	0.8561	0.7258
L-Aspartic acid in an aqueous solution of di-sodium tartrate at mB= 0.5 mol kg^−1
	η 0 = 1.4178 mPa s	η 0 = 1.1996 mPa s	η 0 = 0.9924 mPa s	η 0 = 0.8446 mPa s
0.00638	1.4186	1.2005	0.9931	0.8448
0.00782	1.4188	1.2008	0.9933	0.8453
0.00982	1.4193	1.2011	0.9936	0.8456
0.01307	1.4199	1.2013	0.9939	0.8460
0.01509	1.4203	1.2017	0.9942	0.8462
0.01639	1.4209	1.2021	0.9944	0.8465
L-Aspartic acid in an aqueous solution of di-sodium tartrate at mB= 0.75 mol kg^−1
	η 0 = 1.6087 mPa s	η 0 = 1.3980 mPa s	η 0 = 1.1562 mPa s	η 0 = 0.9866 mPa s
0.00547	1.6099	1.3990	1.1570	0.9873
0.00739	1.6102	1.3992	1.1573	0.9875
0.01025	1.6107	1.3999	1.1577	0.9878
0.01347	1.6111	1.4001	1.1580	0.9881
0.01664	1.6115	1.4005	1.1583	0.9885
L-Aspartic acid in an aqueous solution of tri-sodium citrate at mB= 0.1 mol kg^−1
	η 0 = 1.2165 mPa s	η 0 = 0.9856 mPa s	η 0 = 0.8023 mPa s	η 0 = 0.6650 mPa s
0.00576	1.2170	0.9862	0.8029	0.6655
0.00754	1.2172	0.9865	0.8031	0.6656
0.01002	1.2175	0.9868	0.8033	0.6658
0.01189	1.2178	0.9871	0.8035	0.6660
0.0152	1.2180	0.9874	0.8037	0.6662
L-Aspartic acid in an aqueous solution of tri-sodium citrate at mB= 0.25 mol kg^−1
	η 0 = 1.4206 mPa s	η 0 = 1.1424 mPa s	η 0 = 0.9460 mPa s	η 0 = 0.7902 mPa s
0.00624	1.4217	1.1431	0.9467	0.7906
0.00784	1.4220	1.1434	0.9469	0.7908
0.01080	1.4224	1.1438	0.9473	0.7912
0.01208	1.4228	1.1442	0.9475	0.7914
0.01490	1.4231	1.1445	0.9478	0.7917
0.01825	1.4234	1.1448	0.9480	0.7921
L-Aspartic acid in an aqueous solution of tri-sodium citrate at mB= 0.5 mol kg^−1
	η 0 = 1.7327 mPa s	η 0 = 1.4619 mPa s	η 0 = 1.2096 mPa s	η 0 = 1.0194 mPa s
0.00597	1.7340	1.4631	1.2103	1.0199
0.00809	1.7344	1.4634	1.2107	1.0204
0.00985	1.7347	1.4638	1.2111	1.0207
0.01284	1.7352	1.4640	1.2114	1.0209
0.01520	1.7356	1.4644	1.2118	1.0212
0.01810	1.7361	1.4649	1.2120	1.0215
L-Aspartic acid in an aqueous solution of tri-sodium citrate at mB= 0.75 mol kg^−1
	η 0 = 1.9928 mPa s	η 0 = 1.7555 mPa s	η 0 = 1.4983 mPa s	η 0 = 1.2697 mPa s
0.00626	1.9941	1.7569	1.4992	1.2703
0.00788	1.9946	1.7574	1.4999	1.2709
0.01082	1.9952	1.7578	1.5003	1.2712
0.01180	1.9958	1.7582	1.5007	1.2717
0.01461	1.9964	1.7587	1.5011	1.2720
L-Glutamic acid in water
0.01104	1.1404	0.8921	0.7205	0.5974
0.01308	1.1407	0.8923	0.7209	0.5976
0.01522	1.1411	0.8927	0.7214	0.5978
0.02078	1.1417	0.8932	0.7218	0.5982
0.02517	1.1422	0.8937	0.7221	0.5986
0.03030	1.1429	0.8942	0.7225	0.5990
L-Glutamic acid in an aqueous solution of di-sodium tartrate at mB= 0.1 mol kg^−1
0.01288	1.1646	0.9525	0.7789	0.6650
0.01523	1.1653	0.9534	0.7797	0.6655
0.01930	1.1661	0.9543	0.7803	0.6661
0.02496	1.1669	0.9549	0.7810	0.6666
0.03127	1.1676	0.9556	0.7815	0.6670
0.03591	1.1681	0.9564	0.7820	0.6675
L-Glutamic acid in an aqueous solution of di-sodium tartrate at mB= 0.25 mol kg^−1
0.01410	1.2443	1.0262	0.8556	0.7250
0.01537	1.2450	1.0268	0.8563	0.7257
0.01930	1.2459	1.0275	0.8567	0.7262
0.02391	1.2464	1.0281	0.8571	0.7268
0.03000	1.2471	1.0287	0.8577	0.7273
0.03235	1.2478	1.0296	0.8583	0.7278
L-Glutamic acid in an aqueous solution of di-sodium tartrate at mB= 0.5 mol kg^−1
0.01228	1.4199	1.2015	0.9935	0.8452
0.01354	1.4209	1.2023	0.9944	0.8462
0.01654	1.4217	1.2029	0.9952	0.8469
0.02018	1.4223	1.2034	0.9958	0.8475
0.02585	1.4230	1.2043	0.9963	0.8481
0.03703	1.4238	1.2052	0.9971	0.8488
L-Glutamic acid in an aqueous solution of di-sodium tartrate at mB= 0.75 mol kg^−1
0.01159	1.6114	1.4004	1.1582	0.9877
0.01375	1.6125	1.4011	1.1588	0.9886
0.01765	1.6131	1.4017	1.1592	0.9895
0.01995	1.6139	1.4027	1.1602	0.9904
0.02676	1.6149	1.4036	1.1608	0.9908
L-Glutamic acid in an aqueous solution of tri-sodium citrate at mB= 0.1 mol kg^−1
0.01247	1.2182	0.9874	0.8036	0.6660
0.01463	1.2188	0.9878	0.8039	0.6663
0.01634	1.2193	0.9882	0.8043	0.6667
0.02218	1.2198	0.9889	0.8050	0.6671
0.02857	1.2205	0.9893	0.8055	0.6676
0.03390	1.2212	0.9899	0.8060	0.6682
L-Glutamic acid in an aqueous solution of tri-sodium citrate at mB= 0.25 mol kg^−1
0.01213	1.4232	1.1442	0.9474	0.7914
0.01438	1.4237	1.1446	0.9479	0.7919
0.01771	1.4243	1.1457	0.9484	0.7924
0.02308	1.4250	1.1462	0.9490	0.7929
0.02531	1.4257	1.1467	0.9497	0.7934
0.03401	1.4271	1.1475	0.9507	0.7938
L-Glutamic acid in an aqueous solution of tri-sodium citrate at mB= 0.5 mol kg^−1
0.01104	1.7359	1.4646	1.2114	1.0211
0.01239	1.7362	1.4652	1.2122	1.0217
0.01547	1.7370	1.4659	1.2129	1.0223
0.02012	1.7381	1.4670	1.2138	1.0227
0.02521	1.7392	1.4677	1.2144	1.0239
0.03006	1.7410	1.4686	1.2154	1.0246
L-Glutamic acid in an aqueous solution of tri-sodium citrate at mB= 0.75 mol kg^−1
0.01088	1.9955	1.7581	1.5003	1.2716
0.01408	1.9973	1.7596	1.5010	1.2726
0.01532	1.9978	1.7604	1.5017	1.2735
0.02000	1.9991	1.7614	1.5034	1.2740
0.02799	2.0009	1.7626	1.5050	1.2752
0.03107	2.0019	1.7636	1.5057	1.2766

---

3.3.1. Viscosity B-coefficient. The relative viscosities are given by

η_r = η/η₀ (15)

where, η and η₀ are the viscosities of the solution and solvent, respectively. The B-coefficients were evaluated by fitting the η_r values to the Jones–Dole equation⁴³via a least squares method as follows:

η_r = 1 + BC (16)

where C is the molar concentration (calculated from the molality and density data). The viscosity B-coefficient or B value provides knowledge about the solvation behaviour of solutes. The B values of ASP and GLU in water at 298.15 K are in line with the literature values.¹⁴ The B values for the studied amino acids in water and in aqueous solutions of DST and TSC increase with temperature and with the molality of the co-solutes and they are given in Table S7.† The increase is greater in the case of TSC compared to DST. As the B-coefficient is directly dependent upon the size of the solute, the B value of GLU is slightly greater compared to ASP. Moreover, due to the greater ionic strength of TSC, the observed B values are larger compared to DST. The increase in the B values with the DST and TSC solution concentrations indicates a progressively more structured environment.

The derivative of the B-coefficient with respect to T (dB/dT) is a far better parameter for investigating the effects of additives on the structure of water, because it provides better information about the structure-making or structure-breaking behavior of the solute compared with the B-coefficient. A positive value of dB/dT indicates that a solute is a structure-breaker, whereas a negative value indicates that a solute is a structure-maker.⁴⁴ The dB/dT values for ASP and GLU in water and in aqueous solutions of DST and TSC at different temperatures are given in Table S7.† The dB/dT values for ASP and GLU are positive in water and in aqueous DST and TSC solutions, which classifies these solutes as structure-breakers due to the dominating effects of the hydrophilic groups (–NH₂ and –COOH) over the R-groups.

3.3.2. Viscosity B-coefficient of transfer, Δ_trB. The viscosity B-coefficients of transfer, Δ_trB, from water to aqueous DST and TSC solutions have been calculated as follows:

Δ_trB = B-coefficient (in aqueous DST/TSC solution)-B- coefficient (in water). (17)

The B-coefficient values for the ASP and GLU amino acids in aqueous solutions of DST and TSC are higher than the values in water, which results in positive Δ_trB values. Plots of the Δ_trB values as a function of the DST and TSC molality are shown in Fig. 4(c, f, i, l). The transfer values increase with an increase in the concentration of DST/TSC. For both solutes, the Δ_trB values decrease with temperature in both aqueous DST and TSC solutions. The Δ_trB values have greater magnitudes in the case of TSC, which may again be attributed to the high charge density.

3.3.3. Ratio of the B-coefficient to the partial molar volume, B/V_2,ϕ⁰. The solvation can be judged by the ratio of the B-coefficient to the partial molar volume (B/V_2,ϕ⁰). Unsolvated spherical species have B/V_2,ϕ⁰ values ranging between 0 and 2.5.¹⁴ Solvated spherical species have B/V_2,ϕ⁰ values higher than 2.5. In the present study, the lesser magnitudes of the B/V_2,ϕ⁰ values of the studied amino acids in the presence of the co-solutes compared to in water indicate that these amino acids are more solvated in water (Table S7†).

3.4. Enthalpy measurements from calorimetry

The q values for ASP/GLU (30 mmol kg⁻¹) in the absence, as well as in the presence, of aqueous solutions of DST and TSC over an m_B range from 100–500 mmol kg⁻¹ at T = 298.15 K have been measured using ITC. Positive q values for the solutes have been observed in water and in the presence of TSC/DST, whereas in some cases involving DST, negative q values have also been observed (Table 7). These values decrease with the molality of the solutes in water and increase in the presence of the co-solutes. The Δ_dilH⁰ values (Table S8†) have been calculated by fitting the q and m_A data to the following equations:

q = Δ_dilH⁰ + m_AS_w (18)

q = Δ_dilH⁰ + m_AS_w1 + m_A²S_w2 + ... (19)

where S_w is the slope obtained via linear regression. In some cases, Δ_dilH⁰ values have been obtained using high order polynomial fitting with the constants S_w1, S_w2, etc. Positive Δ_dilH⁰ values, except for ASP in 100 mM DST and GLU in 100 and 250 mM DST, are observed for the studied amino acids in aqueous media and in the presence of the co-solutes. The positive Δ_dilH⁰ values indicate the dominance of dehydration effects over hydrophilic–ionic/hydrophilic interactions. These dehydration effects encourage their use to prevent against microbial activity. Negative Δ_dilH⁰ values indicate the predominance of hydrophilic–ionic/hydrophilic interactions. The magnitude of endothermicity for ASP/GLU is greater in the case of TSC than in the case of DST, which is in accordance with the greater dehydration effects of TSC compared to DST. This shows that hydrophilic–ionic/hydrophilic interactions are more predominant in the case of DST.

Table 7 Enthalpy of dilution values, q, of aqueous solutions of L-aspartic acid and L-glutamic acid in water and in aqueous solutions of di-sodium tartrate and tri-sodium citrate at a T value of 298.15 K and P = 101.3 kPa

m A/mmol kg^−1	q/J mol^−1
	m B = 0 mmol kg^−1	m B = 100 mmol kg^−1	m B = 250 mmol kg^−1	m B = 500 mmol kg^−1	m B = 100 mmol kg^−1	m B = 250 mmol kg^−1	m B = 500 mmol kg^−1
The standard uncertainties, u, are u(m) = 2.8·10^−4 mol kg^−1, u(q) = 0.5 kJ mol^−1, u(T) = 0.03 K, and u(P) = 0.5 kPa.
L-Aspartic acid in an aqueous solution of di-sodium tartrate					L-Aspartic acid in an aqueous solution of tri-sodium citrate
0.05897	2331.13	−445.97	1478.99	1412.85	2981.24	3639.50	5972.42
0.35207	1928.97	116.10	1553.81	1366.52	3057.06	3758.56	6016.78
0.64226	1120.55	607.86	1638.12	1309.33	3208.70	3843.82	6063.55
0.92955	707.04	961.64	1708.83	1264.60	3285.24	3932.01	6113.76
1.21394	538.85	1196.41	1772.46	1249.85	3345.96	3995.34	6156.42
1.49542	450.80	1354.93	1822.87	1227.90	3481.98	4032.45	6214.78
1.77400	393.72	1449.52	1871.82	1215.09	3571.76	4136.79	6251.32
2.04968	351.35	1514.27	1926.90	1244.20	3661.63	4165.05	6306.43
2.32246	317.49	1549.66	1986.88	1273.96	3736.21	4183.07	6347.57
2.59233	286.92	1587.42	2050.69	1335.26	3839.65	4259.48	6396.35
2.85929	263.99	1618.50	2123.13	1445.36	3905.29	4307.43	6452.41
3.12336	238.77	1655.39	2188.19	1518.47	3987.36	4361.31	6488.21
3.38452	228.07	1678.46	2299.31	1603.81	4084.03	4485.43	6537.78
3.64278	209.37	1677.83	2398.92	1708.21	4179.06	4562.62	6577.24
3.89813	198.41	1677.24	2456.84	1802.71	4256.64	4622.75	6627.50
4.15058	183.65	1697.28	2512.35	1915.64	4342.19	4726.03	6665.68
4.40013	168.35	1698.79	2561.23	2008.51	4432.38	4812.32	6705.08
4.64677	164.13	1698.79	2606.28	2090.75	4508.28	4868.91	6749.22
4.89051	154.10	1704.97	2703.05	2171.57	4565.64	4934.77	6798.33
L-Glutamic acid in an aqueous solution of Di-sodium tartrate					L-Glutamic acid in an aqueous solution of tri-sodium citrate
0.05897	397.36	−953.53	−868.11	345.92	1126.24	3303.28	4329.99
0.35207	339.42	−479.12	−816.65	423.73	1194.15	3343.50	4411.15
0.64226	274.18	−67.00	−772.47	469.41	1256.93	3391.24	4510.22
0.92955	251.38	145.23	−714.45	555.31	1314.97	3441.71	4593.43
1.21394	216.36	248.50	−662.62	644.28	1414.14	3491.56	4659.79
1.49542	179.98	306.75	−628.30	697.72	1465.35	3537.03	4727.20
1.77400	160.58	352.91	−592.38	753.07	1556.91	3589.88	4792.46
2.04968	141.98	394.64	−536.11	850.51	1635.86	3641.27	4837.82
2.32246	122.06	417.21	−502.91	902.46	1692.17	3696.22	4900.68
2.59233	105.23	431.29	−475.78	949.48	1768.96	3750.99	4945.44
2.85929	94.52	456.15	−437.47	999.15	1852.31	3807.83	5001.87
3.12336	72.25	487.66	−384.81	1045.31	1917.93	3849.69	5042.00
3.38452	58.34	490.60	−355.74	1094.73	1973.39	3908.89	5115.39
3.64278	42.74	493.88	−315.97	1190.22	2064.57	3953.95	5176.35
3.89813	36.68	478.74	−280.04	1237.70	2142.39	3998.64	5224.55
4.15058	28.84	499.50	−236.68	1275.55	2256.46	4032.62	5272.35
4.40013	19.63	501.58	−194.97	1326.44	2323.28	4079.62	5345.51
4.64677	10.21	504.97	−153.45	1382.78	2392.10	4130.85	5397.24
4.89051	4.70	504.22	−125.31	1448.78	2468.88	4180.52	5466.93

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The Δ_trΔ_dilH⁰ values, i.e., the standard molar enthalpy of transfer, for the studied amino acids, from water to DST/TSC_(aq.) are evaluated using the equation:

Δ_trΔ_dilH⁰ = Δ_dilH⁰ (in DST/TSC_(aq.)) − Δ_dilH⁰ (in water). (20)

Negative Δ_trΔ_dilH⁰ values for ASP in 100 mM TSC, ASP in DST and GLU in DST at all molalities, and positive Δ_trΔ_dilH⁰ values for ASP in 250 mM and 500 mM TSC and GLU in TSC at all molalities have been observed (Fig. S2, ESI†). The more positive magnitudes of the Δ_trΔ_dilH⁰ values in the case of GLU than ASP are due to the presence of an extra –CH₂ (hydrophobic) group. The negative Δ_trΔ_dilH⁰ values suggest the dominance of hydrophilic-ionic/hydrophilic interactions and positive Δ_trΔ_dilH⁰ values may be due to the predominance of co-solute dehydration effects. Overall, the positive Δ_trΔ_dilH⁰ values in the case of TSC (greater dehydration effects) and the negative Δ_trΔ_dilH⁰ values in the case of DST coincide with the results obtained from the volumetric studies.

3.5. Analysis of NMR spectra

¹H spectra have been recorded for ASP and GLU in the absence, as well as in the presence, of DST and TSC using a Bruker (AVANCE-III, HD 500 MHz) spectrometer at a probe temperature of 300.15 K. D₂O was used for the deuterium lock and its signal at 4.650 ppm was taken as the internal reference for the other nuclei. The NMR spectra of ASP and GLU in water (m_A = 0.01 and 0.02 mol kg⁻¹) and in the presence of aqueous solutions of DST and TSC (m_B = 0.75 mol kg⁻¹) have been examined in 9 : 1 H₂O–D₂O solution. The changes in chemical shifts (δ) in ppm are summarized in Table 8.

Table 8 ¹H data for L-aspartic acid and L-glutamic acid in water and in aqueous solutions of di-sodium tartrate and tri-sodium citrate

T = triplet, Q = quartet, M = multiplet.

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In the ¹H NMR spectra of ASP and GLU in aqueous solutions of DST and TSC (m_B = 0.75 mol kg⁻¹), the protons go upfield compared to in the D₂O : H₂O system (Fig. S3†). This shows that the hydrogen bonding of the solutes with water molecules decreases in the presence of DST/TSC owing to the dominance of dehydration effects over hydrophilic–ionic/hydrophilic interactions.

4. Conclusions

Volumetric, acoustic, viscometric, calorimetric and NMR spectroscopic studies have been performed in the present study. The values of Δ_trV_2,ϕ⁰, Δ_trK_2,ϕ⁰ and Δ_trB suggest that hydrophilic–ionic/hydrophilic interactions dominate in the present study. The sweet tastes of both amino acids decrease in the presence of the studied preservatives. The values of the interaction parameter predict pairwise interactions between the amino acids and preservatives. Volumetric and viscometric results indicate that the amino acids behave as structure-breakers in both salt solutions, except in the case of GLU in TSC at m_B = 0.1 mol kg⁻¹. The hydration number and B/V_2,ϕ⁰ values suggest that these amino acids are more solvated in water. Calorimetric and spectroscopic results support the fact that these preservatives stimulate the effects of dehydration on the studied amino acids.

Abbreviations

GLU	L-Glutamic acid
ASP	L-Aspartic acid
DST	Disodium tartrate
TSC	Trisodium citrate
DSA	Density and sound velocity meter
ITC	Isothermal titration calorimetry
NMR	Nuclear magnetic resonance

Conflicts of interest

The authors declare that there are no conflicts of interest.

Acknowledgements

One of the authors (Aashima Beri) is grateful to the Department of Science and Technology, New Delhi for the award of an Inspire Fellowship. The authors also acknowledge the DST-PURSE scheme of the Department of Science and Technology, New Delhi and the UPE-Scheme of the University Grants Commission, New Delhi for research facilities.

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Footnote

† Electronic supplementary information (ESI) available: DETAILS. See DOI: 10.1039/c9fo00872a

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