Measurement and correlation of phase equilibria for DMAM- TBAM as a random amphiphilic copolymer with
polyethylene glycol and KH
2PO
4Masoumeh Foroutan, Marmar Haghighi Khomami
Department of Physical Chemistry, Faculty of Chemistry, College of Science, University of Tehran, Tehran, Iran.
Abstract
In this work, liquid-liquid equilibrium (LLE) of aqueous two-phase systems (ATPSs) containing a synthesized amphiphilic copolymer (DMAM-TBAM), polyethylene glycol (PEG) and KH2PO4 at 338.15K were studied. Furthermore, the extended Flory-Huggins with an electrostatic term (the Debye-Hukel) was used for correlation the experimental data of the quaternary system.
Keywords: Phase behavior; DMAM-TBAM copolymer; PEG; Extended Flory- Huggins theory; Quaternary system.
Introduction
When two polymers or one polymer and one salt are mixed in water above certain concentration, two immiscible aqueous phases was formed. One phase is rich in polymer and the other phase is rich in the other polymer or salt, thus the type of systems were called aqueous two-phase systems (ATPSs) [1]. In the present work, we report liquid-liquid equilibrium data for the aqueous solution containing the amphiphilic copolymer, PEG4000
and potassium dihydrogen phosphate system at 338.15K and a new extended Flory- Huggins theory with the Debye-Huckel equation was developed and was used for LLE data of quaternary system. DMAM-TBAM copolymer is containing two parts: a water- soluble hydrophilic monomer (N, N-dimmethylacrylamide) (DMAM) and a water- insoluble hydrophobic monomer (t-butylacrylamide) (TBAM) [2].
Flory-Huggins model extended to quaternary systems
The activity coefficients of the components in the system can be written as:
k k k
kk' kk' kk'
ln γ = ln γ Lr + ln γ Sr
In this work, for the long- rang electrostatic interaction was used the extended DH equation [3] to calculated lnykLr (Only the second contribution must be added). For short- rang interaction contribution of polymer solutions, extended Flory-Huggins model was used. For a quaternary mixture of polymer (1), copolymer (2), salt (3) and water (4), we consider that a molecule of polymer, copolymer, salt and water occupy r1 , r2 , r3 and r4 =1 lattice sites, respectively. Similar to Ref. [4] we assumed z13 = z23 = 0.
For such a mixture, the activity of any species k can be calculated from
lna1 = ln ϕ1 +1- ϕ1 + r1χ12ϕ2 + r1χ14ϕ4 - r1χ12ϕ1ϕ2 - r1χ14ϕ4ϕ1 - r1χ24ϕ2ϕ4 - r1χ34ϕ4ϕ3 lna2 = ln ϕ2 +1-ϕ2 + r2χ24ϕ4 + r2χ12ϕ1 - r2χ14ϕ1ϕ4 - r2χ34ϕ3ϕ4 - r2χ12ϕ2ϕ1 - r2χ24ϕ2ϕ4 lna 3 = ln ϕ 3 + 1 - ϕ3 + r3 χ 34ϕ 4 - r3 χ13ϕ1ϕ3 - r3 χ 34ϕ3ϕ 4 - r3 χ12ϕ1ϕ 2 - r2 χ 24ϕ
2ϕ 4 lna4 = lnϕ4 +1-ϕ4 + r4χ14ϕ1 + r4χ34ϕ3 + r4χ24ϕ2 - r4χ14ϕ1ϕ4 - r4χ34ϕ3ϕ4 - r4χ12ϕ1ϕ2 - r4χ24ϕ2ϕ4
J1, J2, J3 and J4 are the fractions of lattice sites occupied by the polymer, copolymer, salt and water and the values for rk were calculated using rk=Vk/V4, V is the molar volume of component. For KH2PO4, using the partial molar volume data from the explained method in Ref. [5]. The V1 and V2 value were calculated using a group contribution method [6].
However, these parameters are temperature-dependent according to the following relation:
b1 '
χ ' = b0 ' + kk
kk kk T
The coefficients b0 and b1 are adjustable constants. b0 is independent to temperature and is related to an entropic term. b1kk' is dependent to temperature and is related to an entalpic term.
We can now apply the phase equilibrium condition for the ATPS, i.e., for bottom (bot) and top phases at constant temperature T and pressure P, for any species k in both phases:
top =
k bot
k
The interaction parameters are evaluated from the fitting of experimental LLE data to
µ µ
(
4 N top top2
) (
ot b bot)
2Fob =
∑∑
[ Wk ,l ,exp − Wk ,l ,calk =1 l =1
+ Wk ,l,exp − Wk ,l,cal ]
where Wk,l is the weight percent of the component k for the lth tie-line.
Experimental result of a quaternary system
The liquid-liquid equilibrium LLE data of the quaternary system PEG4000 + DMAM- TBAM copolymer (with molecular weight of 1700 gmol-1) + KH2PO4 +H2O at 338.15K were determined. The ratios of PEG to copolymer were determined by H1NMR to calculated tie - line data and the tie-line data was given in Table 1. The top phase was rich in polymers while the bottom phase was rich in salts.
The binodal curve and tie lines of a quaternary system containing aqueous DMAM- TBAM copolymer +PEG + KH2PO4 were illustrated in Figure1.The interaction parameters were obtained and given in Table 2 and the calculated corresponding deviation was equal to 0.45.
Table.1. Experimental phase equilibrium data for DMAM-TBAM +PEG + KH2PO4 system at 338.15K.
Top Bot
%WP % WS %WP % WS
14.50 5.60 2.40 21.00
18.00 3.20 2.50 22.60
22.00 2.20 3.42 23.00
30 24 18 12 6
0
0 5 10 15 20 25 30
Ws%
Figure 1. the binodal and tie lines for a quaternary system DMAM-TBAM +PEG + KH2PO4
system at 338.15 K.
Wp%
Table.2. Interaction parameters b kk ' of the extended Flory-Huggins + DH equations with Dev 0.45.
T b012 b112 b014 b114
338.15K -188.919 205.409×107 -127.120 501.897×106
b024 b124 b034 b134
-150.215 15.179×107 -162.120 879.129×105
Dev = (Fob /6N) where N is the number of tie-lines.
Conclusion
The new experimental data of liquid-liquid equilibrium for aqueous two phase systems PEG +KH2PO4 + DMAM-TBAM + water at 338.15K have been determined. Furthermore the extended Flory-Huggins model with an electrostatic term (the Debye-Huckel) has been used to correlate the phase behavior of these systems. With these models, we can find the interaction parameters between of polymer, copolymer, salt and water.
Also the concentration of PEG + DMAM-TBAM in both phases was determined by refractive index measurements performed at 338.15K using a refractometer. The relation between the refractive index, n, and the mass fractions of polymer, Wp and salt, Ws is given by:
n = a0 + a1w p + a2w s
It needs to be mentioned, Wp is contained of polymer (1) and copolymer (2) . The values of coefficients a0, a1, and a2 at 338.15K for two phases, top and bottom phases were listed in Table 3.
Table.3. The values of coefficients a0, a1 and a2 at 338.15K for two phases.
Phase a0 a1 a2
Top Bottom
0.12 0.08
0.96 0.79
0.84 0.97
References:
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5. Y. Marcus, J. Chem. Soc., Faraday Trans. 89 (1993) 713- 718. 6. R. Zana, J. Polym. Sci. 18 (1980) 121-126.
