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A New Model and Equation Derived From Surface Tension and Cohesive Energy Density of Coagulation Bath Solvents for Effective Precipitation Polymerization of Acrylonitrile You Zhou1,♠, Liwei Xue1, Kai Yi1, Li Zhang1, Seung Kon Ryu2 and Ri Guang Jin1

1State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Beijing 100029, China2Jeonju Institute of Machinery and Carbon Composites, Jeonju 561-844, Korea

Received 21 May 2012Accepted 5 June 2012

*Corresponding AuthorE-mail: jin.riguang@163.com

Open Access

pISSN: 1976-4251 eISSN: 2233-4998

Carbon Letters Vol. 13, No. 3, 182-186 (2012)Original Articles

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Copyright © Korean Carbon Society

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Abstract A new model and resultant equation for the coagulation of acrylonitrile monomers in precipitation polymerization are suggested in consideration of the surface tension (γ) and cohesive energy density (ECED). The equation was proven to be quite favorable by considering figure fittings from known surface tensions and cohesive energy densities of certain organic solvents. The relationship between scale value of surface tension (γ/M) and cohesive energy density of monomers can be obtained by changing the coagulation bath component for effective precipitation polymerization of acrylonitrile in wet spinning.

Key words: surface tension, cohesive energy density, precipitation polymerization, coagu-lation bath

1. Introduction

Surface tension (γ) is a type of force caused by unbalanced molecular attraction on a liquid surface; it has effects in all dimensions. The direction of surface tension is tangent with the liquid surface, and is vertical to the division line of the two phases. If the liquid surface is planar, the surface tension is right on this plane. On the other hand, if the liquid surface is a curved one, the surface tension is on a tangent plane [1]. Cohesive energy density (ECED) is a physical quantity used to characterize the strength of the interactive force between molecules of a substance [2]. Molecular weight (Mw) is the sum of all atomic mass in the chemical formula; it is related to the surface tension and the cohesive energy density of a substance. A number of empirical equations have been reported for the relationship between the surface tension and the cohesive energy density; the most attractive one of these was proposed by Hildebrand and Scott, as follows [3,4] :

(1)

where V is the molar volume of the substance.This equation is only suitable for non-associated small molecular systems; it is not suitable

for large molecular systems with hydrogen bonds [3]. Therefore, a new equation, suitable for both systems, is necessary.

In this study, a new model and the resulting equation for monomer coagulation are suggested in order to obtain a promising relationship between γ and ECED; many organic solvents that are used as coagulation bath solvents were applied to confirm the equation.

DOI: http://dx.doi.org/ 10.5714/CL.2012.13.3.182

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A New Model and Equation for Effective Precipitation Polymerization of Acrylonitrile

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(2)

When the nascent precipitation monomer coagulates with two other monomers, F(N) will be proportional to the square of [N], and the coagulation rate constant of the second monomer will be half that of the first monomer in its contribution to coagulation. Therefore, F(N)2 can be expressed as the following equation.

(3)

When the nascent precipitation monomer coagulates with three other monomers, F(N) will be proportional to the cube of [N], and the coagulation rate constant of the third monomer will be one-third that of the first monomer in its contribution to coagulation.

(4)

When the nascent precipitation monomer coagulates with n other monomers, F(N) will be proportional to [N]n, and the co-agulation rate constant of the nth monomer will be one-nth that of the first monomer in its contribution to coagulation.

(5)

If there was no monomer to coagulate, F(N) will be proportional to [N]0, and can be expressed as the following equation.

2. Theory

Fig. 1 shows a new schematic model of the surface tension between monomers during coagulation in a bath.

Because surface tension (γ) has a close relation with molecular weight (M), we introduce a new concept, shown in Fig. 1, to establish a comparable relation between monomers. The scale value of the surface tension (γ/M), defined by the surface tension per unit of molecular weight, can be applied to determine the relationship between the surface tension and the cohesive energy density. This scale value of surface tension is related to the lateral tension of the surface molecules, which in turn is related to the cohesive energy inside the liquid [1]. The scale value of the surface tension increases with the increase of the cohesive energy density, as shown in Eq. (1). Cohesion between molecules is the main source leading to surface tension. Suppose there is a liquid droplet and its volume and surface area tend to be minimized due to the cohesion and surface tension. Droplet monomers can be coagulated layer after layer from the center to the surface, as shown in Fig. 2.

The above model can be divided into the following processes and can be applied for the precipitation polymerization of acry-lonitrile in coagulation bath solvent.

Suppose N is the concentration of nascent coagulates at time T; it then can be noted as [N], and the reaction constant of the core monomer and the other monomers can be noted as kij, in which i represents the dimension, and j refers to the serial number of monomers, as shown in Fig. 3.

Then, the following hypothesis can be suggested. F(N) is the number of coagulated monomers in the multi-dimensional direction in the precipitation polymerization. When the nascent monomer coagulates with another monomer, F(N) will be proportional to [N], as shown in the following equation.

Fig. 1. Schematic model of surface tension interaction between monomers.

Fig. 2. Model of liquid droplet coagulation.

Fig. 3. Coagulation of monomers in precipitation polymerization.

Carbon Letters Vol. 13, No. 3, 182-186 (2012)

DOI: http://dx.doi.org/10.5714/CL.2012.13.3.182 184

(13)

In the abovementioned formula, A0 and K0 are constants concerning molecule structure [5].

3. Results and Discussion

The surface tensions and cohesive energy densities of some organic materials that can be used as coagulation bath solvents were obtained from Mark [6]; these values are listed in Table 1. Data were applied to Eq. (13) and obtained relationships between ln(γ/M) and ECED are shown in Fig. 4.

In Fig. 4, three different linear lines were obtained, showing the three different groups. Groups I, II, and III represented alkanes, carboxyl acids, and hydroxyl alcohols, respectively. The slope of group I is negative, while the slopes of group II and group III are positive. This indicates that the surface tension of alkanes decreased with the increase of the cohesive energy density due to the greater dispersion force, which means that the surface tension decreased with the increase of the non-polarity [1]. Similar results for the surface tension of alkanes were re-ported [7]. On the other hand, in carboxyl and hydroxyl groups, the surface tension increased with the increase of the cohesive energy density, which means that the surface tension can be increased with the decrease of the polarity. The constants in Eq. (13) were obtained from the slopes of the three groups; these values are arranged in Table 2.

According to Eq. (13), when ECED tends to zero,, which means the greater A0, the greater

the limit of γ/M ; in certain M conditions, the limit is greater, that is, the smaller the polarity of the solvent, the greater the limit of the surface tension. In Eq. (13), Ko is the slope of the line; the greater the mean of Ko, the greater the impact of the polarity of the solvent on the value of γ/M .

From these results, surface tension and cohesive energy density of coagulation bath solvents can be controlled by changing the mixing ratio of coagulation bath components. And, an effective

(6)

Therefore, all the coagulated nascent monomers will be the summation of F(N)1+ F(N)2 ----- + F(N)n, and the relationship between F(N) and [N] can be obtained as follows.

(7)

If each nascent precipitation monomer has the same ability for precipitation and kij is the function of temperature, it can be thought that kij=kji=k00=k11=…knn=k, and Eq. (7) can be simplified, as follows.

(8)

This equation is exactly part of the Taylor series ek[N] expansion. Therefore, Eq. (8) can be changed to the following form:

(9)

And, the total number of coagulated nascent precipitation monomers is

(10)

where Q is the quantity of precipitates (%), K1 is the constant, and K2 is reaction rate constant.

It is obvious that there is a natural progression relationship between the total number F(N) and the concentration of nascent precipitation monomers (N). Also, the size of N directly relates to the size of the cohesive energy; that is, the greater the cohesive energy, the greater the number of cohesions, and therefore,

(11)

And since F(N) is related to γ/M, the following equation can be obtained.

(12)

This is equivalent to the phenomenological concept: with the cohesive energy density changing, the scale value of the surface tension is proportional to its value:

Fig. 4. Relationships between ln (γ/M) and ECED.

A New Model and Equation for Effective Precipitation Polymerization of Acrylonitrile

185 http://carbonlett.org

the cohesive energy density. We confirmed the correctness of the equation by applying some known organic solvents. With the model and the equation, the effective precipitation polymerization of a PAN precursor can be carried out by controlling the mixing ratio of coagulation for the bath solvent components in consideration of their surface tension, cohesive energy density, and polarity during the wet spinning of acrylonitrile.

References

[1] Wang ZL, Zhou YP, Li SL. Physical Chemistry, Higher Education Press, Beijing, 152-164 (2001).

[2] Jin RG, Hua YQ. High Polymer Physics, Chemical Industry Press, Beijing, 56-61 (2000).

[3] Hu FZ, Chen GR. Material Surface and Interface, East China Uni-versity of Technology Press, Shanghai, 101-102 (2007).

precipitation polymerization of the polyacrylonitrile (PAN) precursor can be obtained from a well controlled mixing ratio of coagulation bath solvents during the wet spinning of acrylonitrile.

4. Conclusions

A new coagulation model for monomers and the resultant equation are suggested; these relate to the surface tension and

Table 1. Surface tensions and cohesive energy densities of some organic materials [6]

Substance Surface tension(γ) mN/m

Cohesive energy density (ECED) J/m3*10-6 Molecular weight (M) ln(γ/M)

n-octane 21.62 243.36 114.22 -1.665

n-butane 16.70 193.21 58.12 -1.247

n-pentane 16.05 204.49 72.15 -1.503

n-hexane 18.40 222.01 86.18 -1.544

n-heptane 20.14 228.01 100.21 -1.605

Nonane 22.85 237.16 128.26 -1.725

n-dodecane 25.35 262.44 170.33 -1.905

Methyl cyclohexane 23.85 256.00 98.18 -1.415

Cyclohexane 25.24 282.24 84.16 -1.204

Formic acid 37.67 615.04 46.03 -0.200

Acetic acid 27.59 428.49 60.05 -0.778

Propionic acid 26.69 412.09 74.08 -1.021

Butyric acid 26.51 462.25 88.11 -1.201

Valeric acid 27.13 404.01 102.13 -1.326

Acrylonitrile 27.22 457.96 53.06 -0.667

1-amyl alcohol 25.79 497.29 88.15 -1.229

n-butyl alcohol 25.38 542.89 74.12 -1.072

Cyclohexanol 33.40 542.89 100.16 -1.098

2-Propanol 21.32 552.25 60.10 -1.036

1-propyl Alcohol 23.71 590.49 60.10 -0.930

Ethanol 22.27 676.00 46.07 -0.727

Methanol 22.45 882.09 32.04 -0.356

Ethylene glycol 48.43 894.01 62.07 -0.248

Dimethyl sulphoxide 43.60 750.76 78.12 -0.583

Table 2. Constants of Eq. (13), obtained from Fig. 4

Group Ao Ko

Alkane -0.62 -0.0092

Hydroxyl -2.38 0.0023

Carboxyl -2.56 0.0042

Carbon Letters Vol. 13, No. 3, 182-186 (2012)

DOI: http://dx.doi.org/10.5714/CL.2012.13.3.182 186

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Springer, New York, 341-349 (2007). [7] Zou LZ, Wang XL, Wang GJ. J Hebei Normal Univ (Nat Sci), 2, 20

(1996).

[4] Wang ZH, Fu JF. A new equation of surface tension of liquid mix-tures. Chem Eng, 4, 1 (1983).

[5] Zhang J, Bu FJ, Dai YQ, Xue LW, Xu ZX, Ryu SK, Jin RG. Experi-mental and theoretical investigations of PAN molecular weight in-crease in precipitation polymerization as a function of H2O/DMSO