Molecular Weight Distribution of Liquid Phase AN and Solid Phase Polymer in Precipitation Polymerization of AN By Changing Solution Composition and Temperature Weiwei Liu, Shuangkun Zhang, Jing Wang, Seung Kon Ryu and Ri-guang Jin Fabrication and Cell Culturing on Carbon Nanofibers/Nanoparticles Reinforced Membranes for Bone-Tissue Regeneration Xu Liang Deng and Xiao Ping Yang Original Articles Carbon Letters Vol. 13, No. 3, 182-186 (2012) A New Model and Equation Derived From Surface Tension and Cohesive Energy Density of Coagulation Bath Solvents for Effective Precipitation Polymerization of Acrylonitrile You Zhou 1,, Liwei Xue 1, Kai Yi 1, Li Zhang 1, Seung Kon Ryu 2 and Ri Guang Jin 1 1 State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Beijing 100029, China 2 Jeonju Institute of Machinery and Carbon Composites, Jeonju 561-844, Korea Article Info Received 21 May 2012 Accepted 5 June 2012 *Corresponding Author E-mail: jin.riguang@163.com Open Access DOI: http://dx.doi.org/ 10.5714/CL.2012.13.3.182 This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/ by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. VOL. 13 NO. 3 July 31 2012 REVIEWS carbonlett.org pissn: 1976-4251 eissn: 2233-4998 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 (E CED ). 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, coagulation 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 (E CED ) is a physical quantity used to characterize the strength of the interactive force between molecules of a substance [2]. Molecular weight (M w ) 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) KCS Korean Carbon Society http://carbonlett.org pissn: 1976-4251 eissn: 2233-4998 Copyright Korean Carbon Society 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 E CED ; many organic solvents that are used as coagulation bath solvents were applied to confirm the equation. 182
A New Model and Equation for Effective Precipitation Polymerization of Acrylonitrile Fig. 1. Schematic model of surface tension interaction between monomers. 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 acrylonitrile 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 k ij, 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. 2. Model of liquid droplet coagulation. 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. 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. When the nascent precipitation monomer coagulates with n other monomers, F(N) will be proportional to [N] n, and the coagulation rate constant of the n th monomer will be one-n th that of the first monomer in its contribution to coagulation. If there was no monomer to coagulate, F(N) will be proportional to [N] 0, and can be expressed as the following equation. (2) (3) (4) (5) Fig. 3. Coagulation of monomers in precipitation polymerization. 183 http://carbonlett.org
Carbon Letters Vol. 13, No. 3, 182-186 (2012) 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. (6) If each nascent precipitation monomer has the same ability for precipitation and k ij is the function of temperature, it can be thought that k ij =k ji =k 00 =k 11 = k nn =k, and Eq. (7) can be simplified, as follows. (7) Fig. 4. Relationships between ln (γ/m) and ECED. This equation is exactly part of the Taylor series e k[n] expansion. Therefore, Eq. (8) can be changed to the following form: And, the total number of coagulated nascent precipitation monomers is (8) (9) (10) where Q is the quantity of precipitates (%), K 1 is the constant, and K 2 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: (13) In the abovementioned formula, A 0 and K 0 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 E CED 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 reported [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 E CED tends to zero,, which means the greater A 0, 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 DOI: http://dx.doi.org/10.5714/cl.2012.13.3.182 184
A New Model and Equation for Effective Precipitation Polymerization of Acrylonitrile Table 1. Surface tensions and cohesive energy densities of some organic materials [6] Substance Surface tension(γ) mn/m Cohesive energy density (ECED) J/m 3 *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 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 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 University of Technology Press, Shanghai, 101-102 (2007). 185 http://carbonlett.org
Carbon Letters Vol. 13, No. 3, 182-186 (2012) [4] Wang ZH, Fu JF. A new equation of surface tension of liquid mixtures. Chem Eng, 4, 1 (1983). [5] Zhang J, Bu FJ, Dai YQ, Xue LW, Xu ZX, Ryu SK, Jin RG. Experimental and theoretical investigations of PAN molecular weight increase in precipitation polymerization as a function of H 2 O/DMSO ratio. Carbon Lett, 11, 22 (2010). [6] Mark JE. Physical Properties of Polymers Handbook. 2nd ed., Springer, New York, 341-349 (2007). [7] Zou LZ, Wang XL, Wang GJ. J Hebei Normal Univ (Nat Sci), 2, 20 (1996). DOI: http://dx.doi.org/10.5714/cl.2012.13.3.182 186