Measurementand correlation ofsolid–liquid phase equilibria forbinary and ternary systems consisting of N-vinylpyrrolidone,2-pyrrolidone and water

Ao Su,Sifang Li*

Department of Chemical and Biochemical Engineering,College of Chemistry and Chemical Engineering,Xiamen University,Xiamen 361005,China

1.Introduction

N-vinylpyrrolidone(NVP,CAS No.88-12-0)is an important monomer for the manufacture of polyvinylpyrrolidone which has extensive applications in the fields of pharmaceuticals,food additives,personal care products,etc.[1].NVP is industrially synthesized by vinylation of 2-pyrrolidone(2-P,CAS No.616-45-5)with acetylene under pressure in the presence of basic catalysts,such as hydroxides and alkoxides[2].The product obtained after fractional distillation usually comprises NVP in an amount of from 99.0%to 99.8%,unreacted 2-P,butane,butadiene,butyne,and amine derivatives,thereinto,the main impurity is 2-P.However,this purity level is unsuitable for the above purposes[3].Moreover,the energy consumption of fractional distillation increases rapidly with the increase ofproductpurity.Then crystallization is gradually used to upgrade industrial grade NVP to pharmaceutical grade NVP,which is more than 99.9%pure,and often more than 99.99%pure[4].The process would be improved by adding a small proportion of water to NVP to be puri fied.The optimum water content is within the range of 1wt%to 2 wt%based on the amount of NVP[5].Although some NVP puri fication technologies based on crystallization have been developed,there are still no solid–liquid equilibria(SLE)data of binary and ternary systems consisting of NVP,2-P and water available on literature,which play a crucial role in the puri fication of NVP by crystallization.

In this work,the SLE of binary NVP+2-P,NVP+water and 2-P+water systems and ternary NVP+2-P+1wt%or 2 wt%water(based on the total mass of NVP and 2-P,the same below)systems were determined.The ideal solubility and the UNIFAC models were applied to predict the SLE,while the Wilson and NRTL models were employed in correlating the experimental data.

2.Experimental

2.1.Materials

Commercial NVP and 2-P were kindly provided by Zhangzhou Hua Fu Chemical Industry Co.,Ltd.(China)with purities of mass fraction higher than 0.999 and 0.995,respectively.All reagents were used as received without any further puri fication.Their purities were tested by gas chromatography(Agilent 7890A)equipped with a flame ionization detector(FID).Deionized water was used in all experiments.The major information about the materials used in this work is listed in Table 1.The experimental melting points were measured using the method in this work(detail in the following ‘Apparatus and procedures’).

2.2.Apparatus and procedures

A method[9–12]for the SLE measurements was used in this work.Fig.1 shows the schematic diagram of the SLE experimental system.It consisted of a triple-jacketed glass still,a cryostat,a magnetic stirrer and a temperature measuring system.A mixture of known composition was contained in the equilibrium cell which maintained atdesired temperature by circulating cryogenic fluid,and a nitrogen atmosphere in the cell was used to avoid humidi fication.The exterior vacuum jacketofthe outside ofthe stillwas used for insulation purposes and visualobservation.A magnetic stirrer bar was placed in the center of the cell achieving continuous stirring by a magnetic stirrer(IKA,model HS7).The samples were prepared gravimetrically using an analytical precision electronic balance(Mettler Toledo,model AL204)with an uncertainty of 0.0001 g.The temperatures of the systems were controlled by a cryostat circulator(Voshin,model DC-2010)which circulated a cryogenic fluid consisting of ethylene glycol and water.A platinum resistance thermometer was immersed into the equilibrium cell and the temperatures were recorded by a digital temperature readout box(ASL,model F250)with a precision of±0.05 K.

Table 1 Sample description①

Fig.1.Schematic diagram of the SLE determination system.

The sample was cooled atthe rate of4 K·h-1untilcompletely solidi fication.An estimate ofthe equilibriumtemperature was obtained fromthe plateau of the cooling curve(temperature versus time).In this study,a degree of supercooling was observed for all samples.The final temperature was maintained constantfor1 h to eliminate the difference oftemperature between sample and bath.Then the sample was heated with a very slow rate(1 K·h-1),the accurate equilibrium temperature was determined by monitoring the gradient of the rate of temperature change in the heating curve[11].Allmeasurements were repeated three times to ensure reproducibility in the determination of the equilibrium temperatures.

3.Models

The thermodynamic relationship for the SLE of a eutectic system with an ideal solid phase can be expressed as follows[13]:

where xiisthe mole fraction ofcomponent i;γiis the activity coefficient;R is the universal gas constant;ΔfusHiis the molar enthalpy of fusion;ΔCpis the difference between the molar heat capacity in the liquid and solid state.Eq.(1)is usually simpli fied as follows[13]:

The value of γican be calculated by the Wilson,NRTL and UNIFAC models.

3.1.The ideal solubility model

Assume that the solution is ideal,then γi=1[14,15],and the ideal solubility xiis obtained from Eq.(2):

3.2.The Wilson model

The Wilson model is expressed as follows[16,17]:

where V1and V2are the liquid molar volumes of pure component1 and 2,λijis energy parameter,Λijis binary parameter.The Wilson modelhas two adjustable parameters:Δλ12(=λ12-λ11)and Δλ21(=λ21-λ22).

3.3.The NRTL model

The NRTL equations are presented as follows[18,19]:

where g12and g21are energy parameters,α12is a parameter related to nonrandomness in the mixture.In this work,α12was set to be 0.3 according to Renon's rules.If α12is assigned,the NRTL model will have two adjustable parameters:Δg12(=g12-g22)and Δg21(=g21-g11),which are independent of temperature and composition.

The adjustable parameters for each binary mixture are calculated by using Marquardt's maximum neighbor method of minimization of the objective function,Fobj,between the calculated and experimentally determined activity coefficients[20]:

3.4.The UNIFAC model

The activity coefficientofcomponent i,γi,in a multicomponentmixture is formulated using the sum ofthe combinatorialpart,lnγiC,and the residual part,lnγiR,as follows[21,22]:

where

where θiis the area fraction,?iis the segment fraction,riand qiare,respectively,measures of molecular van der Waals volumes and molecular surface areas,calculated as the sum of the group volume and area parameters,Rkand Qk,as follows:

In Eq.(18),denotes the number of groups oftype k in molecule i.

where Γkis the group residual activity coefficient;is the residual activity coefficient of group k in a reference solution containing only molecules of type i;θmis the group area fraction;Xmis the group mole fraction;Ψnmis the group-interaction parameter;and anmis the group interaction parameter.

In this study,NVP is composed by 1 molecule of subgroup CH2,1 molecule of subgroup CH2=CH2,1 molecule of subgroup CH2CO and 1 molecule ofsubgroup CH2N;2-P iscomposed by 1 molecule ofsubgroup CH2,1 molecule of subgroup CH2CO and 1 molecule of subgroup CH2NH;water is composed by 1 molecule of subgroup H2O.The values of the group volume and area parameters Rkand Qkare given in Table 2,and the group interaction parameters anmare shown in Table 3[23].Moreover,in order to evaluate the ideal solubility,Wilson,NRTL and UNIFAC models,the mean absolute deviations(Δ)and the relative deviations(σr)on equilibrium temperature are used and expressed as follows[24]:

Table 2 The group volume and area parameters Rk and Qk of the UNIFAC model

Table 3 Group interaction parameters anm of the UNIFAC model

4.Results and Discussion

The measured liquidus temperatures(TL)of all combinations(mole fractions)of binary systems of NVP+2-P,NVP+water,2-P+water and ternary systems of NVP+2-P+1 wt%of water,NVP+2-P+2 wt%of water are reported in Table 4.The uncertainties of the measurements for experimentally determined compositions and temperatures are estimated as±0.0005 mol fraction and±0.2 K,respectively.Figs.2 to 6 are the corresponding phase diagrams(temperature T versus mole fraction x1).

For binary systems,it can be concluded that the phase diagrams for NVP+2-P(Fig.2)and NVP+water(Fig.3)correspond to simple eutectic type.The corresponding eutectic mole compositions(x1E)were 0.5427 and 0.3722,and the eutectic temperatures(TE)were 263.75 K and 251.65 K,respectively.However,the SLE phase diagram is complicated for 2-P+water system(Fig.4).There are two minima(x1E=0.1236,TE=259.15 K;x1E=0.7831,TE=286.15 K)and one maximum(x1C=0.4997,TC=303.55 K)on the liquidus curve of 2-P+water system,thatisto say,the SLE diagramofthis system has two eutectic points and one congruent melting point,inferring that a congruently melting addition compound is formed.The similar situations are also exhibited in the binary systems of 2,4-dinitrophenol+naphthalene[25],t-butanol+p-chlorophenol[26],benzene+hexa fluorobenzene[27]and tbutanol+phenol[28].The molecular representation of this congruently melting addition compound can be calculated as follows[28]:

so the congruently melting addition compound is 2-P·H2O.Thus,there is a formation of two eutectics,one is between water and 2-P·H2O and the other is between 2-P·H2O and 2-P.

Table 4 Experimental SLE data(liquidus temperatures T L)for three binary systems and two ternary systems at mole fraction x1①

Fig.2.SLE phase diagram for binary system of NVP(1)+2-P(2):points,experimental data;solid line,the ideal solubility model;dash line,the Wilson model;dot line,the NRTL model;dash dot line,the UNIFAC model.

Fig.3.SLE phase diagram for binary system of NVP(1)+water(2).

For ternary system NVP(1)+2-P(2)+water(3),two isopleth cuts(verticalsections)were performed:=1%and=2%,in other words,mass fractions of water ω3=0.0099 and 0.0196.The phase diagrams for NVP(1)+2-P(2)+1 wt%water(3)and NVP(1)+2-P(2)+2 wt%water(3)were also the simple eutectic type,the mass eutectic composition(×1)and eutectic temperature(TE)was 0.5031 and 260.25 K at=1%,0.4684 and 256.55 K at=2%.

The parameters in the Wilson and the NRTL models for the binary system of NVP+2-P were obtained from fitting the experimental data using MATLAB software and summarized in Table 5.Activity coefficients of NVP and 2-P obtained from the Wilson,NRTL and UNIFAC modelas wellas experiments were listed in Table 6.Although allthe activity coefficients are close to 1,the calculated activity coefficients by the Wilson model are closest to the experimental activity coefficients.The calculated SLE phase diagrams of the binary system of NVP+2-P from the ideal solubility,the Wilson,the NRTL and the UNIFAC models are plotted in Fig.2.Table 5 also presents the mean absolute deviations(Δ)and the relative deviations(σr)between the experimental and the calculated equilibrium temperatures.For the binary system of NVP+2-P,the best description of SLE was given by the Wilson model with a relative deviation of 0.15%.The results of correlation or predictions using other models showed the relative deviations of 0.16%,0.45%and 0.53%for the NRTL,the UNIFAC and the ideal solubility models,respectively.

Fig.4.SLE phase diagram for binary system of 2-P(1)+water(2).

Fig.5.SLE phase diagram forternary system ofNVP(1)+2-P(2)+1 wt%water(3):points,experimental data;solid line,the UNIFAC model;dash line,the ideal solubility model.

Fig.6.SLE phase diagram forternary system ofNVP(1)+2-P(2)+2 wt%water(3):points,experimental data;solid line,the UNIFAC model;dash line,the ideal solubility model.

Table 5 Optimally fitted binary parameters and the mean absolute deviations(Δ)and the relative deviations(σr)of the ideal solubility,Wilson,NRTL and UNIFAC models for NVP(1)+2-P(2)binary system

The ideal solubility and the UNIFAC models were employed in predicting SLE of the ternary system NVP+2-P+water.Table 7 presents the calculated and experimental activity coefficients of NVP and 2-P.The calculated activity coefficients are consistent with the experimental activity coefficients.The calculated SLE phase diagrams of the systems NVP(1)+2-P(2)+1 wt%water(3)and NVP(1)+2-P(2)+2 wt%water(3)from the ideal solubility and the UNIFAC modelsare plotted in Figs.5 and 6.The UNIFAC model gives better predictions of SLE with the relative deviations of 0.39%and 0.38%for the systems NVP(1)+2-P(2)+1 wt%water(3)and NVP(1)+2-P(2)+2 wt%water(3),respectively(Table 8).

Table 6 Activity coefficients for the binary system NVP(1)+2-P(2)at mole fraction of NVP x1: and,the experimental activity coefficients of NVP and 2-P,respectively;andthe calculated activity coefficients of NVP and 2-P by the Wilson,NRTL and UNIFAC model

Table 6 Activity coefficients for the binary system NVP(1)+2-P(2)at mole fraction of NVP x1: and,the experimental activity coefficients of NVP and 2-P,respectively;andthe calculated activity coefficients of NVP and 2-P by the Wilson,NRTL and UNIFAC model

x1 EXP Wilson NRTL UNIFAC γ1exp γ2exp γ1 cal γ2cal γ1 cal γ2 cal γ1 cal γ2cal 0.0000 1.0000 1.0000 1.0000 1.0000 0.0784 1.0111 1.0010 1.0012 1.0002 0.1613 1.0171 1.0046 1.0050 1.0008 0.2475 1.0284 1.0112 1.0122 1.0019 0.3377 1.0386 1.0217 1.0234 1.0037 0.4071 1.0448 1.0329 1.0351 1.0054 0.4939 1.0508 1.0511 1.0539 1.0079 0.5349 1.0551 1.0618 1.0646 1.0092 0.5427 1.0552 1.0640 1.0668 1.0094 0.5640 1.0507 1.0567 1.0453 1.0089 0.6413 1.0403 1.0394 1.0302 1.0065 0.7236 1.0312 1.0240 1.0177 1.0041 0.8069 1.0209 1.0121 1.0085 1.0021 0.8735 1.0144 1.0053 1.0036 1.0010 0.9519 1.0042 1.0008 1.0005 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000

Table 7 Activity coefficients for the ternary systems NVP(1)+2-P(2)+water(3)at mole fraction ofNVP x1: and,the experimentalactivity coefficients ofNVP and 2-P,respectively;and,the calculated activity coefficients ofNVPand 2-Pby the UNIFACmodel

Table 7 Activity coefficients for the ternary systems NVP(1)+2-P(2)+water(3)at mole fraction ofNVP x1: and,the experimentalactivity coefficients ofNVP and 2-P,respectively;and,the calculated activity coefficients ofNVPand 2-Pby the UNIFACmodel

?

5.Conclusions

Known in this study,the phase diagrams of NVP(1)+2-P(2),NVP(1)+water(2),NVP(1)+2-P(2)+1 wt%water(3)and NVP(1)+2-P(2)+2 wt%water(3)belong to simple eutectic type with the eutectic points at 263.75 K(x1E=0.5427),251.65 K(x1E=0.3722),260.25 K(x1E=0.5031)and 256.55 K(x1E=0.4684),respectively.The binary system of 2-P(1)+water(2)forms a congruently melting addition compound:2-P·H2O,resulting in two eutectic points at 259.15 K(x1E=0.1236)and 286.15 K(x1E=0.7831),and one congruent melting point at 303.55 K(x1C=0.4997).The Wilson model gives the best description of SLE for binary system of NVP+2-P,and the UNIFAC model shows more satisfactory predictions than the ideal solubility model.

Table 8 The mean absolute deviations(Δ)and the relative deviations(σr)of the ideal solubility and UNIFAC models for NVP(1)+2-P(2)+water(3)ternary systems

Nomenclature

anmthe group interaction parameter,K

ΔCpdifference between molar heat capacity in liquid and solid state,J·K-1·mol-1

Fobjobjective function

G adjustable temperature-dependent parameter

g energy parameter of the NRTL model,J·mol-1

ΔfusHmmolar enthalpy of fusion,kJ?mol-1

M molar mass,g?mol-1

m mass fraction

n number of data points

Q group area parameter

q pure component area parameter

R universal gas constant,J?mol-1?K-1

Rkgroup volume parameter

r pure component volume parameter

T temperature,K

u standard uncertainty

V liquid molar volume,cm3·mol-1

number of groups of kind k in a molecule of component i

X liquid phase group fraction

x mole fraction

Z lattice coordination number(=10)

α nonrandomness constant(=0.3)

Γ activity coefficient

γ activity coefficient

Δ the mean absolute deviation,K

θ area fraction

Λ binary parameter of the Wilson model

λ energy parameter of the Wilson model,J·mol-1

σ the relative deviation

τ binary parameter of the NRTL model

Ψnmgroup-interaction parameter

ψ segment fraction

Superscripts

C combinatorial

cal calculation

exp. experiment

i component i

R residual

Subscripts

C congruent melting point;combinatorial

E eutectic point

i,j component i,j

ij pair interaction

k,m,n group k,m,n

L liquidus

m melting point

t triple point

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