Study of Molecular Interactions in the Binary Mixtures of Poly (propylene glycol) diacrylate 800 with 2-MeOH and 2-DMEA- A Computational Analysis

(1)

ISSN 2319-7625 (Online)

(An International Research Journal), www.chemistry-journal.org

Study of Molecular Interactions in the Binary Mixtures of

Poly (propylene glycol) diacrylate 800 with 2-MeOH and

2-DMEA- A Computational Analysis

Sangeeta Sagar and Manisha Gupta

Department of Physics,

University of Lucknow, Lucknow - 226007, U.P., INDIA.

email: [email protected] and [email protected]

(Received on: December 12, 2016)

ABSTRACT

In the present work, volumetric and acoustical methods have been utilized

to study the interactions between Poly (propylene glycol) diacrylate 800 (PPGDA

800) with 2-methoxyethanol (2- Me-OH) and 2-dimethylethanolamine (2-DMEA)

mixtures as a function of temperature and concentration. The density and sound

velocity of pure compounds and their binary mixtures viz. PPGDA 800+2-Me-OH

and PPGDA 800+ 2-DMEA have been measured at temperatures 293.15K, 298.15K,

303.15K, 308.15K and 313.15K at atmospheric pressure. From these parameters,

derived properties such as molar volume (V

m

), Debye temperature (θ

D

), free volume

(V

f

), molecular association (M

A

), non-linearity parameter (B/A), molar sound

velocity (R) and molar compressibility (W) have been calculated. The sound velocity

mixing rules/ theories were also used to test the accuracy of the experimental data.

These results are useful for describing the molecular interactions that exists between

the components in binary mixtures.

Keywords:

density, sound velocity, molar volume, Debye temperature, molecular

association.

1. INTRODUCTION

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any temperature and composition, which provide useful information about molecular structure

and intermolecular forces prevailing in the binary mixtures

1-4

_.

Accumulation of an appropriate amount of experimental data allows drawing

generalized conclusions, deriving appropriate formulas and formulating laws that govern the

studied phenomena. This leads to the possibility to predict and program expected effects for

practical use. Obviously, such a research cycle requires, particularly obtaining information

about molecular interaction and stereochemical effects, the theoretical results to be verified by

experimental results.

In the present work, dilute solutions of Poly(propylene glycol) diacrylate (PPGDA)

800 with 2-methoxyethanol (2-Me-OH) and 2-dimethylethanolamine (2-DMEA) respectively

have been studied thermodynamically at temperatures T= 293.15K, 298.15K, 303.15K,

308.15K and 313.15K over the entire mole fraction range using thermodynamic techniques.

The derived properties such as molar volume (V

m

), Debye temperature (Ө

D

), free volume (V

f

),

non- linearity parameter (B/A), molar sound velocity (R), molar compressibility (W) and

molecular association (M

A

) were calculated from the experimental values of density and sound

velocity. These parameters are quite sensitive towards the interactions between the component

molecules of the mixture. The dependence of these parameters on the composition of the

mixture reveals the nature and extent of interaction between component molecules

5,6

_.

2. EXPERIMENTAL

2.1 Materials

Poly(propylene glycol) diacrylate (PPGDA) Mn= 800 (contains 100 ppm BHT as

inhibitor, 100 ppm MEHQ as inhibitor) ACS reagent, 2-methoxyethanol (2-Me-OH)

Mn=76.10 (anhydrous, ≥99.8%), 2-dimethyethanolamine (2-DMEA) Mn= 89.14 (ACS

reagent, ≥ 99.5%) have been obtained from Sigma Aldrich Chemicals Pvt. Ltd. and no further

purification was done. Structures of compounds used are shown in Figure 1.

Figure. 1 Structure of monomer of PPGDA 800 (a), 2-Me-OH (b) and 2-DMEA (c)

C H₂

O O

O

CH₂ O

n

(a)

(3)

2.2 Mixture Preparation

Mixtures were prepared by weighing the liquids in specially designed ground glass

stopper weighing bottles, taking extreme precautions to avoid contamination and evaporation.

An OHAUS USA (AR2140) single pan balance, with a precision of ±0.1 mg was used

throughout. The maximum possible error in the mole fraction is estimated to be less than

±0.0001.

2.3.1 Sound velocity measurement

The sound velocity

of the pure components and their mixtures were measured with a

variable path, fixed frequency, interferometer provided by Mittal Enterprises, New Delhi

(model-83). It consists of a high frequency generator, a measuring cell, and digital display

micrometer. This interferometer measures the sound velocity of liquids by determining the

wavelength of sound pulses over the distance within the sample using a digital display

micrometer. Measurements of sound velocity were made at a fixed frequency of 2MHz. The

calibration of the interferometer was done by measuring the velocity in AR grade benzene and

CCl

4

with an accuracy of 0.08%. The experiments were replicated at least 5 times for each

PPGDA 800 mixture and the results reported are the average values.

2.4 Density measurement

Densities have been measured by a single capillary calibrated pycnometer made of

Borosil glass, with a bulb capacity of 6.7 ml volume. The pycnometer stem contained

graduation of 0.01ml. Pycnometer was immersed vertically in a double walled cylindrical

water circulated glass jacket. The liquid rise in the capillary of pycnometer was measured by

travelling microscope (having a least count of 0.001 cm) for accuracy. The precision of the

measured densities is of the order of ±1×10

-4

_g.cm

-3

_{. The average of four to five measurements}

was taken for each sample mixtures.

2.5 Temperature maintenance

Circulating water bath with programmable temperature controller (TC-502,

Brookfield Engineering Laboratories, Inc., USA), having variable pump speeds, has been used

for water circulation in water jackets of the apparatuses. The temperature controller covers the

temperature measurement range of 20

o

_{C to 200}

o

_{C, with temperature stability of ±0.01}

o

_C.

3. RESULTS AND DISCUSSION

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Table 1 Comparison of density (ρ) and ultrasonic velocity

(u) with literature data at different

temperatures.

density(g/cm3₎ _{ultrasonic velocity(m/sec)}

Compound T(K) exp. lit. exp. lit.

PPGDA 800 293.15K 1.0186 - 1428.4

-298.15K 1.0138 - 1411.2

-303.15K 1.0107 - 1396.8

-308.15K 1.0067 - 1382.4

-313.15K 1.0021 - 1372.8

-2-Me-OH 293.15K 0.9715 0.9649[a] _1308.0

298.15K 0.9684 0.9603[b]

0.9602[c]

1344.8 1340.2[b]

1341.9[d]

303.15K 0.9623 0.9568[e] _1322.0 _1324.3[e]

308.15K 0.9601 0.9535[a] _1307.2

313.15K 0.9541 1280.4

2-DMEA 293.15K 0.8853 1350.8

298.15K 0.8834 1331.2

303.15K 0.8807 0.8787

0.8793

1318.8

308.15K 0.8759 1308.4

313.15K 0.8732 1297.6

a

_{Ref. [7],}

b

_{Ref. [8],}

c

_{Ref. [9],}

d

_{Ref. [10],}

e

_[11],

The derived properties such as molar volume (V

m

), Debye temperature (Ө

D

), free

volume (V

f

), non- linearity parameter (B/A), molar sound velocity (R), molar compressibility

(W) and molecular association (M

A

) were calculated from following equations.

The molar volume (V

m

) of the mixture can be calculated from the following relation

V

m

=

∑

𝑛_𝑖=1

𝑥

_𝑖

𝑀

_𝑖

/ρ

(1)

where x and M are respectively the mole fraction and molecular weight of the component i.

The non- linearity parameter (B/A) has been defined

12

_{in terms of specific heat ratio}

as:

B/A = 2γK

״

_{+ 2K}

₍₂₎

where K and K

״

are the isobaric acoustical parameters and isochoric acoustical parameters.

Molar compressibility has been calculated using following relationship

(W) = (β

1/7

_V)

₍₃₎

Molar sound velocity as

(R) = (u

1/3

_V)

₍₄₎

(5)

during the mixing of liquids. Suryanarayan and Kuppusami

13,14

_{proposed the following relation}

for free volume in liquids:

2 / 3

f

k

Mu

V



















(5)

Tables 2 and 3 shows the values of molar volume (V

m

), Debye temperature (Ө

D

) and

free volume (V

f

) in varying temperature range for the binary mixture of PPGDA800+

2-Me-OH and PPGDA800+ 2-DMEA respectively.

Table 2. Molar volume (V

m

), Debye temperature (Ө

D

) and free volume (V

f

) for the binary mixture

of PPGDA800+ 2-Me-OH with mole fraction of PPGDA 800 (

x

₁

) at T = (293.15 to 313.15) K.

X1 Molar Volume(Vm) Debye Temp. (ӨD) Free Volume (Vf)

293.15K

0.00000 78.33078 76.91155 0.03894 0.10001 150.35616 62.30800 0.00293 0.20120 221.47789 55.25678 0.00170 0.30003 290.17308 50.84838 0.00104 0.40018 360.9813 47.41403 0.00130 0.49911 431.53668 44.76014 0.00149 0.59946 502.47611 42.59756 0.00176 0.69997 574.01918 40.79478 0.00199 0.79768 642.46731 39.33619 0.00225 0.89953 714.21396 38.03666 0.00245 1.00000 785.33235 36.93483 0.00260

298.15K

0.0000 78.57901 74.88349 0.04747 0.10001 150.01092 61.16617 0.00447 0.20120 221.97561 54.10629 0.00251 0.30003 291.65481 49.73379 0.00185 0.40018 362.68536 46.44042 0.00212 0.49911 433.24642 43.87921 0.00246 0.59946 504.00093 41.85429 0.00282 0.69997 575.37870 40.16169 0.00319 0.79768 644.45915 38.74435 0.00354 0.89953 717.02564 37.48659 0.00405 1.00000 789.04257 36.36621 0.00448

303.15K

0.00000 79.07558 73.46974 0.05577 0.10001 150.18899 60.32735 0.00668 0.20120 222.2967 53.48741 0.00399 0.30003 291.83233 49.28343 0.00269 0.40018 363.82131 45.95522 0.00336 0.49911 434.61400 43.44981 0.00382 0.59946 506.05095 41.40308 0.00445 0.69997 578.11280 39.74348 0.00479 0.79768 647.44748 38.38718 0.00519 0.89953 719.83736 37.11886 0.00579 1.00000 791.51594 36.03511 0.00650

308.15K

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0.30003 294.29218 48.61692 0.00389 0.40018 366.22725 45.26673 0.00476 0.49911 436.88395 42.77685 0.00572 0.59946 508.43417 40.7883 0.00663 0.69997 579.93211 39.15314 0.00757 0.79768 649.93759 37.80409 0.00841 0.89953 722.64915 36.59775 0.00933 1.00000 794.60779 35.59198 0.01023

313.15K

0.00000 79.75836 70.97581 0.07136 0.10001 153.16102 58.20752 0.01466 0.20120 225.59141 51.92959 0.00845 0.30003 294.97768 48.12125 0.00646 0.40018 366.88366 44.94744 0.00755 0.49911 437.93637 42.52968 0.00884 0.59946 510.19947 40.50866 0.00974 0.69997 582.66117 38.89762 0.01100 0.79768 652.42780 37.60214 0.01173 0.89953 725.46119 36.37539 0.01248 1.00000 798.31794 35.36702 0.01391

Table 3. Molar volume (V

m

), Debye temperature (Ө

D

) and free volume (V

f

) for the binary mixture

of PPGDA800+ 2-DMEA with mole fraction of PPGDA 800 (

x

₁

) at T = (293.15 to 313.15) K.

X1 Molar Volume(Vm) Debye Temp. (ӨD) Free Volume (Vf)

293.15K

0.00000 101.83925 68.91469 0.01421 0.10004 169.72578 58.68098 0.00120 0.20018 237.61144 52.91642 0.00121 0.29996 303.41646 49.13295 0.00129 0.39964 372.33844 46.10686 0.00152 0.50550 445.12527 43.65716 0.00184 0.59998 511.27205 41.86022 0.00204 0.70013 581.09666 40.28353 0.00226 0.79912 648.46694 38.99824 0.00236 0.89966 717.88605 37.88004 0.00250 1.00000 785.33235 36.93483 0.00260

298.15K

0.00000 100.89474 68.14505 0.01814 0.10004 170.12705 57.88782 0.00125 0.20018 236.37257 52.36582 0.00154 0.29996 304.36294 48.49454 0.00192 0.39964 374.70239 45.4868 0.00236 0.50550 448.99293 43.01958 0.00271 0.59998 514.10319 41.29512 0.00312 0.70013 585.23321 39.71467 0.00358 0.79912 652.59707 38.47574 0.00388 0.89966 720.71914 37.38413 0.00432 1.00000 789.04257 36.43851 0.00449

303.15K

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0.59998 516.12552 40.8967 0.00422 0.70013 585.06342 39.38399 0.00471 0.79912 653.62970 38.10497 0.00521 0.89966 723.55241 36.98507 0.00575 1.00000 791.51574 36.03511 0.00650

308.15K

0.00000 101.76055 66.80819 0.02895 0.10004 171.46441 56.92234 0.00253 0.20018 237.9043 51.46176 0.00297 0.29996 306.72983 47.61350 0.00349 0.39964 376.47578 44.69722 0.00421 0.50550 451.45436 42.27138 0.00518 0.59998 517.74343 40.53383 0.00628 0.70013 587.80193 38.99816 0.00735 0.79912 656.72763 37.71569 0.00841 0.89966 725.81907 36.59672 0.00920 1.00000 794.60779 35.62290 0.01024

313.15K

0.00000 102.07529 66.19924 0.03466 0.10004 172.26693 56.43918 0.00265 0.20018 239.34828 51.01910 0.00334 0.29996 308.14994 47.25046 0.00436 0.39964 378.24878 44.35002 0.00566 0.5055 453.56373 41.95103 0.00708 0.59998 520.17053 40.23329 0.00842 0.70013 589.62748 38.71935 0.00995 0.79912 658.27609 37.45643 0.01116 0.89966 728.65185 36.32143 0.01261 1.00000 798.31794 35.32585 0.01389

Molecular association (M

A

) is an attractive interaction between two molecules that

results in a stable association in which the molecules are close to each other resulting in the

formation of a molecular complex, which is a loose association of two or more molecules. The

non- linear variation of molecular association (Figure 2) with mole fraction of PPGDA 800

with 2-Me-OH and 2-DMEA interprets presence of specific interaction between the

constituents of the mixtures.

The variation of non-linear parameter (B/A) against mole fraction of polymer shows

non- linear behaviour in table 4. For both the systems PPGDA 800+ 2-Me-OH and PPGDA

800+ 2-DMEA, the values of B/A decreases at lower concentrations and further increase in

concentration indicating a specific interaction which occurs between the systems at all the

temperatures. The non linearity parameter is high for the system PPGDA 800+ 2- DMEA as

compared to the system PPGDA 800+ 2-Me-OH suggesting PPGDA 800 is highly interactive

with 2-DMEA.

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Figure 2. Molecular Association (MA) verses the mole fraction of PPGDA 800 (x1) for binary mixtures: (a) PPGDA 800+ 2- Me-OH and (b) PPGDA 800+ 2-DMEA at 293.15K, 298.15K, 303.15K, 308.15K and 313.15K.

Table 4. Non- Linearity Parameter (B/A) for binary mixture PPGDA 800 + 2- Me-OH and

PPGDA 800+ 2-DMEA with mole fraction of PPGDA 800 (

x

₁

) at T= 293.15K, 298.15K, 303.15,

298.15Kand 313.15 K

PPGDA 800+ 2-Me-OH

X1 293.15K 298.15K 303.15K 308.15K 313.15K

0.00000 -4.69700 -4.55392 -4.37162 -4.24364 -4.08833 0.10001 2.87725 2.86911 2.88883 2.96423 2.99914 0.20120 5.53591 5.50964 5.49415 5.50530 5.49102 0.30003 6.87039 6.82935 6.79534 6.77545 6.74213 0.40018 7.70431 7.64960 7.60784 7.56796 7.52675 0.49911 8.26033 8.19615 8.14689 8.09490 8.04966 0.59946 8.66395 8.59489 8.53943 8.48096 8.43103 0.69997 8.96877 8.89688 8.83772 8.77284 8.72062 0.79768 9.19994 9.12586 9.06438 8.99612 8.94151 0.89953 9.39473 9.31903 9.25319 9.18342 9.12547 1.00000 9.55324 9.47421 9.40644 9.33648 9.27661

PPGDA 800+ 2-DMEA

X1 293.15K 298.15K 303.15K 308.15K 313.15K

0.00000 -1.65825 -1.67303 -1.56795 -1.45363 -1.37163 0.10004 3.55722 3.56737 3.59774 3.61743 3.63828 0.20018 5.74338 5.70020 5.68614 5.67902 5.67391 0.29996 6.93284 6.89679 6.87082 6.84186 6.81630 0.39964 7.70485 7.66294 7.62198 7.57985 7.54378 0.50550 8.26333 8.21393 8.16430 8.11612 8.07255 0.59998 8.62984 8.57121 8.51685 8.46356 8.41522 0.70013 8.92837 8.8656 8.80400 8.74688 8.69324 0.79912 9.16064 9.09404 9.02929 8.96811 8.91125 0.89966 9.35401 9.28283 9.21555 9.14990 9.09099 1.00000 9.51379 9.44005 9.36916 9.30040 9.23881

(a)

(9)

3.2 Computation of sound velocity using various mixing rules

Sound velocity study of liquid and liquid mixtures has been gained much importance

during the last two decades in assessing the nature of molecular interactions and investigating

the physicochemical behavior of such systems

18-20

_.

Nomoto

21

_{, assuming the linearity of the molar sound velocity and the additivity of the}

molar volumes in liquid solutions, gave the following relation

3 2 2 1 1 2 2 1 1 3 m m m V x V x R x R x V R u _               

(5)

Table 5. Molar sound velocity (R) and molar compressibility(W) for binary mixture PPGDA 800

+ 2- Me-OH and PPGDA 800+ 2-DMEA with mole fraction of PPGDA 800 (

x

₁

) at T= 293.15K,

298.15K, 303.15 , 298.15Kand 313.15 K

X1 Molar sound velocity (R )

Molar

compressibility X1

Molar sound velocity (R)

Molar compressibility

PPGDA800+2-MeOH PPGDA800+2-DMEA 293.15K

0.00000 872.08502 1651.27596 0.00000 1125.75933 2102.21918 0.10001 1677.68137 3183.13103 0.10004 1881.73525 3550.65491 0.20120 2478.59215 4709.92595 0.20018 2641.83119 5005.06169 0.30003 3254.76757 6191.18935 0.29996 3381.46903 6425.12608 0.40018 4052.81995 7710.99196 0.39964 4155.96564 7901.61049 0.49911 4848.04059 9223.53109 0.50550 4976.48263 9466.3496 0.59946 5647.25527 10745.67054 0.59998 5723.89835 10887.50431 0.69997 6453.74003 12280.01967 0.70013 6514.87259 12391.84225 0.79768 7226.01715 13752.48560 0.79912 7280.14434 13851.78005 0.89953 8037.48685 15297.87866 0.89966 8072.38159 15359.01543 1.00000 8844.43512 16832.88884 1.00000 8844.43512 16832.88884

298.15K

0.00000 867.34615 1643.58187 0.00000 1109.89775 2076.80528 0.10001 1662.99555 3159.23265 0.10004 1878.02909 3544.65992 0.20120 2467.26909 4691.47714 0.20018 2617.17663 4964.99853 0.30003 3248.98010 6181.75197 0.29996 3378.23842 6419.86417 0.40018 4045.79255 7699.53011 0.39964 4166.2492 7918.36623 0.49911 4836.96693 9205.46991 0.50550 4999.76694 9504.30135 0.59946 5632.82780 10722.13529 0.59998 5732.80759 10902.02817 0.69997 6436.69785 12252.21948 0.70013 6535.0709 12424.76546 0.79768 7213.95352 13732.80379 0.79912 7298.44475 13881.62025 0.89953 8033.11008 15290.73806 0.89966 8071.80924 15358.08201 1.00000 8844.55061 16833.07724 1.00000 8850.40793 16842.63199

303.15K

(10)

308.15K

0.00000 866.6512 1642.45303 0.00000 1112.99431 2081.77073 0.10001 1672.12374 3174.09057 0.10004 1883.64906 3553.74998 0.20120 2478.37143 4709.56643 0.20018 2620.48155 4970.37208 0.30003 3256.55547 6194.10432 0.29996 3386.32006 6433.02594 0.40018 4054.56197 7713.83280 0.39964 4163.31011 7913.57796 0.49911 4840.37559 9211.03007 0.50550 5000.33422 9505.22566 0.59946 5638.62033 10731.58557 0.59998 5741.5810 10916.32745 0.69997 6437.82533 12254.05902 0.70013 6526.45993 12410.73137 0.79768 7221.98134 13745.9017 0.79912 7300.26651 13884.59019 0.89953 8037.73423 15298.28224 0.89966 8076.90136 15366.38622 1.00000 8849.22034 16840.69482 1.00000 8851.78237 16844.87392

313.15K

0.00000 866.08015 1641.52535 0.00000 1113.35643 2082.35127 0.10001 1673.72879 3176.70191 0.10004 1887.98210 3560.75584 0.20120 2477.45945 4708.08096 0.20018 2630.45519 4986.58258 0.30003 3253.66864 6189.39755 0.29996 3394.90432 6447.00135 0.40018 4052.82955 7711.00762 0.39964 4174.03177 7931.04301 0.49911 4843.69680 9216.44706 0.50550 5013.32420 9526.38706 0.59946 5647.11417 10745.4404 0.59998 5756.91204 10941.30714 0.69997 6457.06936 12285.44945 0.70013 6532.98966 12421.37371 0.79768 7239.42182 13774.34983 0.79912 7302.17605 13887.7031 0.89953 8055.69743 15327.58285 0.89966 8091.12735 15389.58193

1 8875.92465 16884.24561 1 8872.47903 16878.62736

Van Dael and Vangeel

22

_{proposed the following ideal mixing relation for predicting}

speed of sound of a binary liquid mixture































2 2 2 2 2 1 1 1 2 m 2 2 1

1

M

u

x

u

M

x

u

1 M

x

M

x

1 (6)

Zhang Junjie

23

_{gave following relation for the sound velocity in a binary mixture}





_           2 2 2 2 2 2 1 1 1 1 2 2 1 1 2 2 1 1 m u ρ V x u ρ V x M x M x V x V x u

(7)

Schaaffs’ relation

24

_{, which is based on the Collision Factor Theory (CFT), for}

predicting sound velocity in pure liquids, has been extended to the binary liquid mixtures by

Nutsch-Kuhnkies and is given as



 



m 2 2 1 1 2 2 1 1 m

V

B

x

B

x

S

x

S

x

u



_



(8)

The values of surface tension obtained by Flory theory have been used to evaluate

sound velocity, making use of the well-known Auerbach relation

25

3 / 2 m 4 m m 10 3 . 6

u _

        _





(9)

(11)

The values of sound velocity evaluated using tables 6 and 7 shows that Van Deal,

Nomoto’s and Junjie’s are in fairly good agreement with the experimental values for both the

systems. The average percentage values for Schaaff’s relations are also within limits of error,

while the average percentage deviation using Flory relation give large deviation for both the systems.

Table 6. Ultrasonic Mixing rules for binary mixture PPGDA 800 + 2- Me-OH with mole fraction

of PPGDA 800 (

x

₁

) at T= 293.15K, 298.15K, 303.15, 298.15Kand 313.15 K

X1 EXPERIMENTAL NOMOTO VANDEAL JUNJIE SCHAAF FLORY

293.15K

0.000000 1380.0 1380.000124 1380.000000 1380.000 1380.0 1358.014 0.100013 1389.2 1389.198861 1036.236531 1403.916 1389.2 1355.005 0.201205 1401.6 1401.599779 894.5751458 1413.353 1401.6 1354.722 0.300029 1411.2 1411.199756 824.653287 1418.261 1411.2 1354.785 0.400175 1415.2 1415.199993 789.6761524 1421.361 1415.2 1355.014 0.499108 1417.9 1417.899773 779.5595800 1423.450 1417.9 1355.574 0.599457 1419.6 1419.600125 791.3155109 1424.988 1419.6 1355.199 0.699968 1421.2 1421.199819 828.6030068 1426.155 1421.2 1355.666 0.797684 1422.8 1422.800074 901.0337622 1427.046 1422.8 1356.596 0.899533 1425.2 1425.199789 1051.195642 1427.794 1425.2 1362.954 1.000000 1428.4 1428.400260 1428.4.0000 1428.400 1428.4 1393.824

APD - 1.07104 -0.40052 -0.400524 3.574425 3.84732

298.15K

0.000000 1344.8 1344.800032 1344.800000 1344.800 1344.8 1338.237 0.100013 1362.4 1362.400566 1009.919466 1376.152 1362.4 1337.397 0.201205 1373.2 1373.200129 871.9783078 1388.558 1373.2 1338.447 0.300029 1382.4 1382.400136 803.9606577 1395.022 1382.4 1339.701 0.400175 1388.1 1388.099541 770.0334089 1399.108 1388.1 1340.723 0.499108 1391.6 1391.600148 760.3924930 1401.864 1391.6 1341.470 0.599457 1396.0 1396.000226 772.1826705 1403.894 1396.0 1342.203 0.699968 1400.0 1399.999973 809.0798334 1405.434 1400.0 1343.818 0.797684 1402.6 1402.599683 880.7040904 1406.611 1402.6 1345.987 0.899533 1406.2 1406.200249 1029.686578 1407.600 1406.2 1354.252 1.000000 1408.4 1408.399817 1408.400000 1408.400 1408.4 1387.850

APD - -3.35964 -0.53296 -0.53296 -1.12548 3.011436

303.15K

0.000000 1322.0 1321.999757 1322.000000 1322.000 1322.0 1328.586 0.100013 1344.0 1343.999780 992.8800454 1358.524 1344.0 1328.067 0.201205 1357.9 1357.899994 857.3550420 1373.163 1357.9 1330.929 0.300029 1369.9 1369.900429 790.5781764 1380.833 1369.9 1333.346 0.400175 1374.8 1374.800101 757.3407240 1385.697 1374.8 1335.140 0.499108 1379.2 1379.199985 748.0215665 1388.983 1379.2 1336.463 0.599457 1382.6 1382.600383 759.8553103 1391.408 1382.6 1337.257 0.699968 1387.4 1387.399973 796.5365150 1393.249 1387.4 1339.834 0.797684 1391.6 1391.599893 867.7096577 1394.658 1391.6 1343.212 0.899533 1394.0 1393.999796 1016.123576 1395.841 1394.0 1351.590 1.000000 1396.8 1396.800204 1396.80000 1396.800 1396.8 1388.121

APD - -1.85741 -0.53327 -0.5337 -6.27984 2.358768

308.15K

(12)

0.599457 1364.0 1363.999751 751.3509103 560.2538 1364.0 1333.694 0.699968 1368.0 1368.000083 787.6226986 532.7372 1368.0 1335.196 0.797684 1372.0 1371.999961 858.0013524 510.9813 1372.0 1338.736 0.899533 1376.0 1375.999726 1004.759684 492.1796 1376.0 1347.819 1.000000 1381.2 1381.199956 1381.200000 476.5886 1381.2 1385.196

APD - 5.01413 1.163631 1.16363 1.66483 1.2598

313.15K

0.000000 1280.4 1280.399821 1280.400000 1280.400 1280.4 1312.001 0.100013 1305.0 1305.000499 961.7770015 1325.853 1305.0 1317.968 0.201205 1324.5 1324.50025 830.647857 1344.305 1324.5 1321.98 0.300029 1342.0 1341.999665 766.1208251 1354.029 1342.0 1325.784 0.400175 1348.0 1347.999611 734.1237982 1360.215 1348.0 1327.293 0.499108 1353.0 1352.999758 725.3670320 1364.405 1353.0 1328.774 0.599457 1356.0 1355.999777 737.2431259 1367.501 1356.0 1329.839 0.699968 1361.0 1360.999789 773.4697821 1369.855 1361.0 1332.764 0.797684 1366.2 1366.199975 843.7127856 1371.656 1366.2 1337.229 0.899533 1369.2 1369.199930 990.8431748 1373.172 1369.2 1347.391 1.000000 1374.4 1374.400228 1374.400000 1374.400 1374.4 1389.813

APD - 4.63331 -0.72981 -0.71289 1.53722 0.742408

Table 7. Ultrasonic mixing rules for binary mixture PPGDA 800+ 2-DMEA with mole fraction of

PPGDA 800 (

x

₁

) at T= 293.15K, 298.15K, 303.15 , 298.15Kand 313.15 K

X1 EXPERIMENTAL NOMOTO VANDEAL JUNJIE SCHAAF FLORY

293.15K

0.00000 1350.8 1350.800112 1350.80000 1350.799 1350.8 1344.346 0.10004 1362.8 1362.79999 1056.133105 1378.196 1362.8 1318.019 0.20018 1374.4 1374.400014 925.8974410 1394.060 1374.4 1310.611 0.29996 1384.2 1384.199957 858.4552700 1404.025 1384.2 1305.873 0.39964 1390.6 1390.599985 825.0649453 1410.834 1390.6 1306.824 0.50550 1397.4 1397.399963 815.8472411 1416.035 1397.4 1308.727 0.59998 1403.2 1403.200023 828.2583961 1419.548 1403.2 1312.527 0.70013 1409.2 1409.200026 865.9293428 1422.487 1409.2 1317.921 0.79912 1415.0 1415.000034 939.2983484 1424.824 1415.0 1325.696 0.89966 1421.8 1421.799991 1083.920604 1426.776 1421.8 1344.149 1.00000 1428.4 1428.399990 1428.400000 1428.402 1428.4 1393.348

APD - -5.73022 -0.8921528 -0.892487 -0.892147 5.11415

298.15K

0.00000 1331.2 1331.20166 1331.200000 1331.200 1331.201 1336.385 0.10004 1345.2 1345.201107 1040.838947 1360.767 1345.200 1316.269 0.20018 1357.4 1357.399555 912.5199542 1377.058 1357.400 1306.060 0.29996 1367.4 1367.400548 846.0851434 1387.102 1367.400 1304.955 0.39964 1374.6 1374.599891 813.2187568 1393.894 1374.600 1307.615 0.50550 1380.8 1380.800266 804.1949085 1399.049 1380.800 1310.122 0.59998 1386.6 1386.599940 816.5049321 1402.516 1386.600 1312.473 0.70013 1392.4 1392.400098 853.7669923 1405.406 1392.400 1318.195 0.79912 1398.8 1398.799779 926.3256419 1407.700 1398.800 1325.534 0.89966 1404.8 1404.800247 1069.459092 1409.610 1404.800 1341.778 1.00000 1411.2 1411.199817 1411.200000 1411.200 1411.200 1389.790

APD - -1.97475 -0.8831071 -0.8831052 -6.58495 4.049161

303.15K

(13)

0.50550 1369.8 1369.799965 796.6380231 1384.946 1369.800 1310.275 0.59998 1374.8 1374.800152 808.8051672 1388.328 1374.800 1312.903 0.70013 1380.4 1380.400176 845.6713755 1391.148 1380.400 1316.734 0.79912 1385.8 1385.800021 917.4637998 1393.385 1385.800 1324.333 0.89966 1391.4 1391.400073 1059.049328 1395.249 1391.400 1341.274 1.00000 1396.8 1396.800226 1396.800000 1396.800 1396.800 1388.121

APD - -1.50682 -0.76102 -0.769104 -5.01281 3.15399

308.15K

0.00000 1308.4 1308.401794 1308.400000 1308.400 1308.401 1337.048 0.10004 1325.8 1325.800222 1022.974668 1335.535 1325.800 1318.633 0.20018 1336.4 1336.399933 896.8180093 1350.626 1336.400 1307.178 0.29996 1345.6 1345.600362 831.4802322 1359.957 1345.600 1306.308 0.39964 1352.4 1352.399769 799.1244630 1366.276 1352.400 1307.552 0.50550 1358.8 1358.799664 790.1772257 1371.076 1358.800 1310.497 0.59998 1363.8 1363.800276 802.1720157 1374.305 1363.800 1313.127 0.70013 1368.8 1368.800236 838.6155065 1376.998 1368.800 1317.291 0.79912 1373.6 1373.600183 909.5973671 1379.136 1373.600 1324.563 0.89966 1378.0 1377.999818 1049.486398 1380.917 1378.000 1340.068 1.00000 1382.4 1382.399956 1382.400000 1382.400 1382.400 1386.245

APD - -1.52974 -0.6110253 -0.611023 -5.08455 2.268166

313.15K

0.00000 1297.6 1297.599487 1297.600000 1297.600 1297.6 1337.417 0.10004 1316.4 1316.400691 1014.545346 1325.344 1316.4 1320.533 0.20018 1327.4 1327.399593 889.4439304 1340.667 1327.4 1309.922 0.29996 1337.2 1337.200477 824.6614861 1350.119 1337.2 1308.804 0.39964 1343.8 1343.799810 792.5933036 1356.512 1343.8 1310.009 0.50550 1350.4 1350.400231 783.7504837 1361.364 1350.4 1313.067 0.59998 1355.6 1355.600205 795.6871928 1364.626 1355.6 1315.823 0.70013 1360.2 1360.199842 831.9005612 1367.347 1360.2 1319.137 0.79912 1365.0 1364.999947 902.4273906 1369.505 1365.0 1326.107 0.89966 1369.2 1369.199729 1041.472159 1371.304 1369.2 1342.188 1.00000 1372.8 1372.800227 1372.800000 1372.800 1372.8 1388.401

APD - -1.59209 -0.548297 -0.548107 -5.24019 1.402448

4. CONCLUSION

The results obtained in the present study show the presence of specific molecular

interactions in PPGDA 800 + 2-Me-OH and PPGDA 800 + 2-DMEA. The order of molecular

interaction is PPGDA 800 + 2-Me-OH < PPGDA 800 + 2-DMEA. The empirical

relations/theories used for estimation of the sound velocity show good agreement with the

respective measured values of sound velocities for the systems PPGDA 800 + 2-Me-OH and

PPGDA 800 + 2-DMEA. Nomoto, Van Deal and Junjie relation exhibit an excellent agreement

between the experimental and theoretical estimated values of sound velocities for both the

binary systems.

5. ACKNOWLEDGEMENT

One of the authors (SS) is thankful to UGC for financial support through Rajiv Gandhi

National Fellowship.

REFERENCES

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