Study on the Bleeding Mechanism of Slip Agents in a Polypropylene Film using Molecular Dynamics

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1 REGULAR CONTRIBUTED ARTICLES M. Wakabayashi 1,2 *, T. Kohno 3, Y. Tanaka 3, T. Kanai 1,2 1 Idemitsu Kosan Co., Ltd., Ichihara, Chiba, Japan 2 Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa, Japan 3 Prime Polymer Co., Ltd., Sodegaura, Chiba, Japan Study on the Bleeding Mechanism of Slip Agents in a Polypropylene Film using Molecular Dynamics The bleeding (internal transport) process of additives in a polypropylene film under atmospheric pressure was investigated. The experimental results were explained more precisely by a new model assuming the two-step transport between the amorphous and crystalline regions. The diffusion coefficient of a higher fatty acid such as behenic acid (docosanoic acid) in isotactic polypropylene film and that of higher fatty acid amides such as erucamaide (13-cis-docosenamide) in ethylene copolymerized polypropylene film were determined at 40 and 508C respectively. The difference between the diffusion coefficients of three slip agents in a polypropylene film at 50 8Cwas explained using a molecular dynamics simulation in which self-association of the slip agent molecules by hydrogen bonding was considered. 1 Introduction * Mail address: Makoto Wakabayashi, Advanced Technology Research Laboratories, Idemitsu Kosan Co., Ltd., 1-1, Anesaki-Kaigan, Ichihara, Chiba, , Japan makoto.wakabayashi@si.idemitsu.co.jp Many additives are used to add more favorable qualities to films, which are widely used as a packaging material. The slip agents give lubrication to a film by bleeding to the film surface. Many articles regarding the solubilities and the diffusions of additives in polymer films were reported (Billingham et al., 1981; Koszinowski, 1986; Schwartz et al., 1989; Spatafore and Pearson, 1991; Földes and Turcsányi, 1992; Földes, 1993, 1994; Möller and Gevert, 1994; Hatashi et al., 1994; Quijada- Garrido et al., 1996a, 1996b; Reynier et al., 2001a, 2001b). However, there seems to be no satisfactory models for bleeding so far. In previous articles (Wakabayashi et al., 2006, 2007a, 2007b, 2007c), a novel two-step transport model for additives such as slip agents and UV-stabilizers was proposed. It was shown that the bleeding process of additives under atmospheric pressure was explained more precisely by assuming the twostep transport process between the crystalline and amorphous regions. The additive in an ipp film dissolves in the amorphous region first, and if the concentration reaches saturation solubility it becomes impossible to dissolve more. The additive that is beyond this saturation solubility migrates to the film surface at a certain speed according to the diffusion process. Furthermore it is known that an ipp film has spherulites and amorphous regions, which are supposed to exhibit different migration speeds in the bleeding process. The spherulites have crystalline regions consisting of folded chain molecules and the additives exist in between the crystalline regions. We considered that the diffusion of a portion of the excess amount of additives beyond the saturation solubility existing in the spherulites was restricted and those additives migrated slowly according to the first-order kinetics. The rest of the excess amount of additives exists in the amorphous regions among spherulites. The extent of restriction within spherulites was assumed to increase with the initial amount of the additives. Accordingly we proposed that the two-step transport model could be expressed as yðtþ ¼ðC 0 C s Þfa þ ð1 aþ½1 expð ktþšg cðx; tþ dxaa; ð1þ 4l l l x cðx; tþ ¼erf p 2 ffiffiffiffiffi l þ x þ erf p Dt 2 ffiffiffiffiffi ; ð2þ Dt where y(t) is the amount of bleeding additive on the film surface at time t, C 0 is the initial concentration of additive, C s is the saturation solubility, a is a diffusion ratio, k is the constant of first-order kinetics, l is the half thickness of film, c(x, t) is the normalized concentration at time t and distance x, erf(x) is the error function and D is the diffusion coefficient. The diffusion ratio a is assumed to be larger at a lower concentration of additive, because the restriction within the spherulites is thought to be weak at a lower concentration. There are big differences in the saturation solubilities and the diffusion coefficients of different slip agents such as erucamide and behenamide based on the two-step transport model. Therefore self-association of slip agents was supposed to occur in the ipp film; however, no evidence of self-association was found. It is still difficult to detect the self-association since only a small amount of slip agent exists in the ipp film. We also showed that the molecular dynamics (MD) simulation was useful for predicting the saturation solubilities and the diffusion coefficients of UV-stabilizers qualitatively. In this paper, a new method for predicting the self association of slip agents in an ipp film using molecular dynamics (MD) simulation will be discussed. Intern. Polymer Processing XXIV (2009) 2 Ó Carl Hanser Verlag, Munich 133

2 2 Experimental 2.3 Molecular Dynamics (MD) Simulation 2.1 Materials Additive-free isotactic polypropylene (ipp, Idemitsu H700) and polypropylene copolymerized with 3.4 wt.% of ethylene (Et-co-PP, Idemitsu R740) were used. H700 has a nominal density of 900 kg/m 3, melt flow rate (MFR) of 7.0 g/10 min, melting temperature (Tm) and heat of melting (DHm) by DSC measurement of C and 98.7 J/g, isotactic pentad fraction evaluated by 13 C NMR spectroscopy of 93.2 mol.%, and average molecular masses estimated by size exclusion chromatography of M n = , M w = and M z = R740 has a nominal density of 900 kg/m 3, MFR of 7.0 g/10 min, Tm and DHm of C and 79.3 J/g, and average molecular masses of M n = , M w = and M z = Behenic acid (docosanoic acid) and erucamide (13-cis-docosenamide) was supplied by NFC Co., Ltd. (Osaka, Japan). 2.2 Sample Preparation and Measurements The blends of PP and slip agents with a small quantity of antioxidant additives (500 ppm of Irganox1076 (Ciba-Geigy) and 500 ppm of Irgafos 168 (Ciba-Geigy)) were prepared by dry mixing and then fed into a single-screw extruder operated at 2008C with a screw speed of 100 min 1. The extruded strands were quenched in cold water and cut into the pellet form. The obtained pellets were fabricated into 50 lm-thick-film using the U (diameter) 40 mm T-die casting machine, wherein the temperature from the bottom of the hopper to the T-die was set from 200 to 230 8C with a screw speed of 80 min 1.The film was chilled at 308C. Several sets of 50 sheets of films with size of 10 cm long and 10 cm wide were prepared. They were put in an oven immediately after fabrication for bleeding measurement under the predetermined temperature and time. Films were taken out from the oven after a predetermined time and put in 500 ml solvent such as acetone for behenic acid and ethanol for erucamide for 5 s and then washed for 5 s. The solvents were removed by using a rotary evaporator. The amounts of the bled additives were determined by size exclusion chromatography with a Waters 410 RI detector (for behenic acid) or gas chromatography with Shimadzu GC-14A (for erucamide). Additive Polymer Temperature 8C Saturation Solubility Cs, ppm The MD simulations were performed using a commercial package, Nanobox software from Nano Simulation Associates, Japan. By using the united atom (UA) model under constant particle number, constant pressure and constant temperature (NPT) condition, temperature was fixed by the Nose-Hoover method and pressure was controlled by Andersen s method. The electrostatic interactions were computed using the spherical Ewald truncation method (Fukuda and Kuwajima, 1997, 1998; Kuwajima et al., 2006). 3 Results and Discussion 3.1 The Bleeding Profile of Slip Agents The experimental results of the amount of bleeding of behenic acid obtained at 50 8C are shown in Fig. 1. The two-step transport model represented by solid lines in the figure explains the bleeding profile of behenic acid well. Table 1 summarizes the parameters obtained from the two-step transport model. The relationship between the saturation solubilities and bleeding temperature and Arrhenius plot of diffusion coefficient are shown in Figs. 2 and 3 respectively. Both saturation solubility and diffusion coefficient of behenic acid are the largest and both val- Diffusion coefficient D, m 2 /s Constant of first-order kinetics k, l/s Diffusion ratio a 1 a 2 a 3 Behenic acid ipp a 0.59 a Erucamide Et-co-PP b 0.84 b 0.63 b Erucamide c ipp Behenamide c ipp Erucamide c ipp the initial concentration of additives (C 0,i ) a C 0,1 : 5,000 ppm, C 0,2 : 7,000 ppm; b C 0,1 : 500 ppm, C 0,2 : 900 ppm, C 0,3 : 1,400 ppm; c Wakabayashi et al., 2007a Table 1. Parameters obtained from a two-step transport model Fig. 1. Amount of bleeding additive versus time for behenic acid in ipp film at 508C. Initial concentration (C 0,i ): C 0,1 = 5000 ppm (&); C 0,2 = 7000 ppm (~), the full lines were calculated by using the twostep transport model 134 Intern. Polymer Processing XXIV (2009) 2

3 Fig. 2. Saturation solubility against temperature for ipp film behenic acid (*); erucamide (~); behenamide (&), the data of erucamide and behenamide were reported in Wakabayashi et al., 2007a Fig. 3. Arrhenius plot as log D against 1/T for ipp film behenic acid (*); erucamide (~) ; behenamide (&), the data of erucamide and behenamide were reported in Wakabayashi et al., 2007a Fig. 4. Amount of bleeding additive versus time for erucamide in Etco-PP film at 408C. Initial concentration (C 0,i ): C 0,1 = 500 ppm (&); C 0,2 = 900 ppm (~); C 0,3 = 1,400 ppm (*), the full lines were calculated by using the two-step transport model ues of behenamide are the smallest. The molar masses of behenic acid (341 g/mol), erucamide (338 g/mol), and behenamide (340 g/mol) are almost the same. On the other hand, experimental results of bleeding suggested that the molecular size of behenic acid is smaller than that of erucamide and the molecular size of erucamide is smaller than that of behenamide. We assume here that the reason for the significant differences between the saturation solubilities and the diffusion coefficients of slip agents is because of the self-association of erucamide and behenamide by hydrogen bonding occurring in ipp film. The size of the self associated molecules should influence both the saturation solubilities and the diffusion coefficients of slip agents. The experimental results and the theoretical fitting curves based on the two-step transport model for the bleeding of erucamide in Et-co-PP film at 408C are shown in Fig. 4. The two-step transport model explains the bleeding profile well. The relationship between the saturation solubilities and bleeding temperature and Arrhenius plot of diffusion coefficient are shown in Figs. 5 and 6 respectively. The saturation solubility of erucamide in ET-co-PP film at 408C was slightly smaller than that of erucamide in ipp film. As described previously, DHm of H700 from DSC measurement was 98.7 J/g while DHm of R740 was 79.3 J/g, indicating that the portion of amorphous region of R740 is larger than that of H700. As the result, it is considered that the miscibility between erucamide and Et-co-PP rather than the crystallinity dominated the bleeding behavior. On the other hand, the diffusion coefficient of erucamide in ET-co-PP film was almost the same as that of erucamide in ipp film. Fig. 5. Saturation solubility of erucamide against temperature R740 (*); H700 (~), the data of H700 were reported in Wakabayashi et al., 2007a Fig. 6. Arrhenius plot of erucamide as log D against 1/T R740 (*); H700 (~), the data of H700 were reported in Wakabayashi et al., 2007a Intern. Polymer Processing XXIV (2009) 2 135

4 Fig. 7. Model compounds for estimating the number of self associated fatty acid amides. The hydrogen bonding by amide group was replaced by the covalent bond of carbon atom (C*) Fig. 8. Typical conformation of ipp/mc-3 blends with five chains of ipp (MM: 50,000) and ten molecules of MC-3 per unit cell 136 Intern. Polymer Processing XXIV (2009) 2

5 3.2 Estimation of the Number of Self-associated Molecules from Molecular Dynamics (MD) Simulation It was shown that there was possibility of forming the self association of fatty acid amide in a PP film. But it is still difficult to detect the number of self associated molecules analytically. Therefore the method to evaluate the number of self associated molecules by using MD simulation was investigated. It was assumed that the structure of a self associated fatty acid amide forms ladder structure by hydrogen bonding. The model compounds (MC) of the self associated fatty acid amide were prepared as shown in Fig. 7. Since it was difficult to estimate the influence of hydrogen bonding by force field parameters of Nanobox, the hydrogen bonding was replaced by the covalent bond of carbon atoms (C*). Five polymer chains with degrees of polymerization of 1200 which has almost the same molar mass ( g/mol) as ipp used in this paper were prepared. Ten molecules of MC-1, MC-2, MC-3 and MC-4 were mixed with ipp in a unit cell respectively. Five molecules of MC-7 were mixed with ipp in a unit cell. The bulk amorphous state of the blends was built using cubic unit cells subjected to periodic boundary conditions. The system was compressed by performing 100 ps duration using a time step of 2 fs under 10 MPa at K. Then the system was equilibrated by performing 2500 ps duration using a time step of 2 fs under 0.1 MPa at K. The main runs were performed 500 ps duration 5 t using a time step of 2 fs under 0.1 MPa at K. Fig. 8 shows the typical conformation of ipp/mc-3 blends with five chains of ipp and ten molecules of MC-3 after main run. The results of MD calculation are shown in Table 2. The densities of these systems which were thought to be an important factor when estimating self diffusion coefficients were consistent with each other. The radius of gyration was calculated using equation below Model compound Density by MD Root mean square radius of gyration d, kg/m 3 Rg, nm P N r k r c:g: 2 Rg 2 k¼0 ¼ ; ð3þ N þ 1 where N is the number of atoms, r k is the position of atom k and r c.g. is the center of gravity of the model compound. The self diffusion coefficient (D self ) was calculated using the equation below 1 D self ¼ lim t!1 6t h j rðt þ t 0Þ rðt 0 Þj 2 i; ð4þ where hjrðt þ t 0 Þ rðt 0 Þj 2 i is the averaged mean square distribution, r(t) is the center of gravity of the model compound. Fig. 9 shows the time dependency of the mean square distribution of MC-3. The values of D self were calculated using five data from 60 to 200 ps as shown in Fig. 9. In Fig. 10 the root mean square radius of gyration is plotted against the number of branched chains on a double-logarithmic scale. The slope was calculated to be Since the number of branched chains is proportional to a molecular weight, it is thought that the MD simulation using model compounds gave a reasonable result. In Fig. 11 the logarithm of diffusion coefficients also gave a straight line as a function of the number of branched chains. By using this relationship, the numbers of self associated molecules of erucamide and behenamide were estimated from the result of the differences of logarithm of the dif- Fig. 9. Mean square distribution of MC-3 as a function of time (*, *, ~, &, &), the straight line shows the averaged least-squares fit by using five data from 60 to 200 ps Fig. 10. Relationship between the root mean square radius of gyration and the number of branched chains of model compounds on a doublelogarithmic scale Self diffusion coefficient by MD D self,m 2 /s MC MC MC MC MC Table 2. Density, root mean square radius of gyration and self diffusion coefficient of model compounds calculated by MD simulation Intern. Polymer Processing XXIV (2009) 2 137

6 Additive Diffusion coefficient at 508C log (D/(m 2 /s)) fusion coefficients between behenic acid and erucamide or behenamide in ipp film at 50 8C in Fig. 3. In the previous article (Wakabayashi et al., 2007b, 2007c), it was mentioned that the calculated values from MD presented the self diffusion coefficients of additives of Brownian motion in the very narrow range of the amorphous state, and the calculated values from the two-step transport model presented relative diffusion coefficients of additives which were thought to be restricted by various barriers when the additives passed from the crystalline regions to the amorphous regions among the spherulites and passed through the amorphous regions among the spherulites to the film surface. But the slope on the double-logarithmic scale plot was calculated to be about 1.0 and a good correlation between the diffusion coefficients from MD and the two step transport model was shown. Therefore it is assumed that 1) behenic acid exists as a single molecule and 2) the difference of calculated self diffusion coefficients of model compounds by MD is consistent with the difference of diffusion coefficients of slip agents obtained from the two-step transport model on a double-logarithmic scale. The estimated values of the number of the self association at 508C were given in Table 3. Since the difference of logarithm of diffusion coefficients between behenic acid and erucamide is 0.75, the number of self associated molecules of erucamide in ipp film at 508C can be estimated at 3.1 from linear relationship in Fig. 11. Similarly the number of self associated molecules of behenamide can be estimated at 7.3. The different number of self associated molecules is thought to cause the different value of diffusion coefficient. It was shown that the MD simulation Difference from log D of behenic acid D log (D/(m 2 /s)) was considered to be useful to estimate the number of self associated molecules by hydrogen bonding which was difficult to evaluate quantitatively. 4 Conclusions A new model for bleeding process of additives in a polypropylene film under atmospheric pressure was investigated. By using the two-step transport model, the saturation solubilities and diffusion coefficients of behenic acid in ipp film at 50 8C and erucamide in Et-co-PP at 40 8C were determined. The two-step transport model explains the bleeding profiles of slip agents well. The differences between the saturation solubilites and the diffusion coefficients of slip agents can be explained by assuming that the self association of molecules by hydrogen bonding occurs in ipp film. By using MD simulation of model compounds, the numbers of self associated molecules of erucamide and behenamide at 508C are estimated at 3.1 and 7.3 respectively. It was shown that the MD simulation was considered to be useful to estimate the number of self associated molecules by hydrogen bonding which was difficult to evaluate quantitatively. References The estimated number of self associated molecule from the linear relationship in Fig. 11 N Behenic acid Erucamide a Behenamide a a Wakabayashi et al., 2007a Table 3. Estimation of the number of self associated molecules from MD simulation Fig. 11. Relationship between the self diffusion coefficients and the number of branched chains of model compounds on a double-logarithmic scale Billingham, N. C., et al., Solubility of Phenolic Antioxidants in Polyolefins, J. Appl. Polym. Sci., 26, (1981) Földes, E., Turcsányi, B., Transport of Small Molecules in Polyolefins. I. Diffusion of Irganox 1010 in Polyethylene, J. Appl. Polym. Sci., 46, (1992) Földes, E., Transport of Small Molecules in Polyolefins. II. Diffusion and Solubility of Irganox 1076 in Ethylene Polymers, J. Appl. Polym. Sci., 48, (1993) Földes, E., Transport of Small Molecules in Polyolefins. III. Diffusion of Topanol CA in Ethylene Polymers, J. Appl. Polym. Sci., 51, (1994) Hayashi, H., et al., Diffusion of Methyl Esters of Higher Fatty Acid in Polypropylene, J. Appl. Polym. Sci., 51, (1994) Fukuda, M., Kuwajima, S., Molecular-dynamics Simulation of Moisture Diffusion in Polyethylene beyond 10 ns Duration, J. Chem. Phys., 107, (1997) Fukuda, M., Kuwajima, S., Molecular Dynamics Simulation of Water Diffusion in Atactic and Amorphous Isotactic Polypropylene, J. Chem. Phys., 108, (1998) Koszinowski, J., Diffusion and Solubility of Hydroxy Compounds in Polyolefines, J. Appl. Polym. Sci., 31, (1986) Kuwajima, S., et al., Molecular-Dynamics Evaluation of Fluid-Phase Equilibrium Properties by a Novel Free-Energy Perturbation Approach: Application to Gas Solubility and Vapor Pressure of Liquid Hexane, J. Chem. Phys., 124, (2006) 138 Intern. Polymer Processing XXIV (2009) 2

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