English

• INTRODUCTION

  Poly(p-phenylene terephthalamide) (PPTA) has been noted as a kind of important polymer materials which presents a combination of outstanding properties such as good chemical resistance, low flammability and excellent mechanical properties^[1]. It also possesses high thermal stability with high melting temperature^[2], and forms highly oriented structure because of their rigid backbones.

  As an important polymer product with growing demand^{[1, 3-5]}, there have been extensive researches focusing on the PPTA synthesis in recent years^[6-8]. The conventional preparation method for PPTA is low temperature solution polycondensation of p-phenylenediamine (PPD) and terephthaloyl chloride (TPC) in a mixed solvent of N-methyl-2-pyrrolidone (NMP) containing CaCl₂, as shown in Scheme 1, which is the most widely used in almost all commercial products, like Kevlar, Twaron, Technora, etc^[9]. CaCl₂ is used to weaken the hydrogen bond interaction between PPTA chains because of the complexation between calcium ion and amidogen. In this cooling polycondensation process, it involves low initial reaction temperature and significant increase of viscosity with the molecular weight growing, resulting in severe difficulty in reactant mixing, also leading to strict temperature control demand and high blending requirements^[10]. Because of the high-activity monomers, this process requires strict dehydration, deoxidation and accurate temperature control. Pyridine is necessarily used for the absorption of HCl because of its alkaline effect, avoiding the side reaction between HCl and PPD. Moreover, the polycondensation will be completed quickly because the activation energy was is low (6.3 kJ/mol). Due to the strongly exothermic nature (reaction enthalpy is -199 kJ/mol)^[11], this process usually results in a rapid increase in the temperature.

  Scheme 1

  

  Scheme 1.  Polycondensation of PPD and TPC for the preparation of PPTA

  DownLoad: Full-Size Img PowerPoint

  PPTA is commonly transformed into high-performance fibers and fabrics to be used as transformed materials and composite materials with superior thermal and mechanical resistance. There is still wide research interest in obtaining PPTA with high molecular weight to be transformed into high tenacity and modulus fibers. However, only about 15% of the theoretical tensile strength has been achieved, while fibers with tensile modulus up to 50%-80% of the theoretical value have been commercialized^[12]. The tensile strength is highly dependent on defects including the chain ends, whereas the tensile modulus is not very sensitive to this. The molecular weight and the obtained chain length have been shown to be directly related to the tensile strength of high modulus polymeric fibers. However, molecular weight cannot be increased without limit by using current technologies because of difficulties in polymerization and processing.

  The polycondensation of PPTA follows the step-reaction mechanism that any two oligomers with the appropriate functional groups can react to form a larger molecule^[13], and become strong diffusion-controlled at the moderate degree of polymerization^[14]. This diffusion effect retards the primary reaction and prevents the formation of high molecular weight polymer due to the capping of functional groups by side reactions that become significant. However, this diffusion-effected kinetics of polycondensation of PPTA is difficult to be detected by experiment because of the fast reaction rate and the orientation constraint of rod-like polymers. A number of previous works have been carried out to study the polymerization kinetics of rod-like molecules under quiescent conditions or well defined flow conditions by means of experiments and theory^[15-23] based on the Smoluchowski' diffusion equation^[24]. It described the polymerization kinetics by using three kinds of diffusion coefficient about the axial direction, radial direction and rotational. Many theories for the rotational and translation diffusion coefficients for the rigid rod-like polymers, like PPTA, in dilute solution modeled the molecule as a smooth cylinder, thus the complex geometry of the molecular surface could be ignored^[25]. These theoretical approaches also assumed "stick" (nonslip) boundary conditions at the surface of the particle. In the semi-dilute solution regime, the theoretical studies were based on the "tube model" proposed by Doi^[26] and the general expression obtained by Teraoka that could be applied in all over the concentration range^{[27, 28]}. Agarwa and Khakhar^[15-17] developed the above theories and studied the polymerization and dynamics of rigid rod-like polymers both in dilution and semi-dilution solution, especially about the condensation polymerization of PPTA. The obtained relationship between reaction rate constant, monomer concentration, degree of polymerization and shearing rate established the foundation for the further study of kinetics research of PPTA. Agge and Khakhar^{[22, 29, 30]} studied the kinetics of solution polymerization to synthesize PPTA theoretically and experimentally under quiescent conditions or extensional flow conditions. These studies presented an integrated kinetics of solution polymerization of PPTA. However, these research works only revealed the polymerization rate constant of polymers with the same chain length, rather than the polydispersed system.

  In this paper, the conventional preparation method for PPTA was described in detail. Since PPTA with higher molecular weight will build up better mechanical properties and thermostability so that can be applied to different application fields, the molecular weight is the most important criterion for PPTA. The effects of different experimental conditions on the inherent viscosity (η_inh) and the number-average degree of polymerization (${\bar X_{\rm{n}}}$) of PPTA, such as reaction time, monomer concentration and initial temperature, were investigated systematically. We also presented the theoretical study and molecular simulation of the diffusion-effected kinetics for the polycondensation in terms of the system parameters. And these predictions of the model were also compared with the experimental results.

  EXPERIMENTAL

  Materials and Equipment

  p-Phenylenediamine (PPD, purity > 99.9%) and terephthaloyl chloride (TPC, purity > 99.9%) were purchased from J & K Chemical Co. Ltd. N-methyl-2-pyrrolidone (NMP, purity > 99.9%), calcium chloride anhydrous (CaCl₂, purity > 96%), pyridine (Py, purity > 99.9%) and sulfuric acid (H₂SO₄, purity > 98%) were all purchased from Sinopharm Chemical Reagent Co. Ltd, China. The trace water in NMP was removed by adding NMP in molecular sieve and CaH₂ before the experiments. CaCl₂ was carefully heated for 4 h at 400 ℃ to dehydrate in a muffle furnace before use. The oxygen content of the nitrogen used in the process is less than 3 ppm.

  The temperature was controlled by a refrigerated circulating bath, which was bought from Shanghai Bilon Instrument Company. An Ubbelohde viscometer with capillary diameter 0.9-1.0 mm was used to measure the inherent viscosity of PPTA at 30 ℃.

  Poly(p-phenylene terephthalamide) Synthesis

  The polymerization was carried out in a jacketed glass reactor. Initially, 500 mL of dried NMP was added into the 2 L reaction vessel, which had been purged by nitrogen to remove oxygen. The reaction system was heated to 78 ℃. Then, finely ground dry CaCl₂ was added into the NMP solution with stirring. After CaCl₂ was completely dissolved, PPD and a certain amount of pyridine were added to the NMP/CaCl₂ solution with stirring. When all PPD and pyridine were completely dissolved, an ice-water bath was used to absorb heat and cool the solution to -10~5 ℃. The polymerization was initiated at this stage by adding powdered TPC under rapid stirring. The TPC was divided into two equal parts and added in sequence to react with PPD with a 10 min interval. The whole reaction process was carried out under a nitrogen atmosphere. The precipitated PPTA was placed in the grinder, and washed with deionized water at high-speed for several times so that the reaction was quenched. Then the polymer was immersed in ethanol for 8 h to remove water and NMP absorbed in PPTA. Finally, the samples were dried overnight under vacuum at 80 ℃ before being tested. The yield of PPTA was higher than 90%.

  Viscosity Measurement

  The molecular weight was measured by inherent viscosity method. The obtained PPTA (0.25 g) was initially dissolved in 98% sulfuric acid at 70 ℃ to prepare a PPTA/H₂SO₄ solution with a concentration of 0.5 g/dL and then measured at (30 ± 0.1) ℃ using an Ubbelohde viscometer. By calculating the ratio of the flow times between solvent and solution, the relative viscosity and consequently the inherent viscosity were determined as a measure for the molecular weight of PPTA. The inherent viscosity was obtained as

  ${\eta _{{\rm{inh}}}} = \frac{1}{c}\ln \left( {{\eta _{\rm{r}}}} \right) = \frac{1}{c}\ln \left( {\frac{t}{{{t_0}}}} \right)$

  where η_inh is the inherent viscosity; η_r is the relative viscosity; t represents the efflux time for the polymer solution (PPTA/H₂SO₄), t₀ represents the efflux time for the 98% sulfuric acid, and c represented the mass concentration of the PPTA/H₂SO₄ solution (g/dL).

  The relationship between inherent viscosity and weight-average molecular weight of PPTA is^[31]

  ${M_{\rm{w}}} = 3165\eta _{{\rm{inh}}}^{{\rm{1}}{\rm{.503}}}$

  where η_inh ranges from 2.6 dL/g to 9.0 dL/g.

  The weight-average degree of polymerization was calculated by

  ${\overline {{\rm{DP}}} _{\rm{w}}} = {M_{\rm{w}}}/238$

  where 238 is the molecular weight of repeat unit of PPTA.

  According to the relationship between the number-average degree of polymerization ($ {\bar X_{\rm{n}}} $) and the extent of reaction (p) as

  ${\bar X_{\rm{n}}} = \frac{1}{{1 - p}}$

  ${\overline {{\rm{DP}}} _{\rm{w}}} = \frac{{1 + p}}{{1 - p}}$

  The number-average degree of polymerization was calculated by

  ${\bar X_{\rm{n}}} = \frac{{{{\overline {{\rm{DP}}} }_{\rm{w}}} + 1}}{2}$

  X-ray Analysis

  X-ray diffraction (XRD) was used to determine the crystal unit cell parameters and the apparent lateral crystal size. The XRD measurements were carried out on a Rigaku X-ray diffractometer (D/MAX-2550PC, Rigaku, Tokyo, Japan). These PPTA samples prepared to be powder were laid on the glass sample holder (35 mm × 50 mm × 5 mm). Ni-filtered Cu Kα radiation (λ = 0.154 nm) generated at a voltage of 40 kV and current of 35 mA was utilized at a scan speed of 5 (°)/min from 5° to 90°. The step-scan method was used to determine the d spacing and stacking size (D). The step-interval was set at 0.02°. The data were analyzed with Peakfit software (version 4.12, Seasolve Co., San Jose, CA). The d space and D were calculated by using Eq. (7) (the Bragg equation) and Eq. (8) (the Scherrer equation), respectively:

  $n\lambda = 2d{\rm{sin}}\theta $

  $D = K\lambda /B{\rm{cos}}\theta $

  in which λ is X-ray wavelength (λ = 0.154 nm), K is the Scherrer constant (= 1.0), and B is the full-width at half-maximum of the reflection measured in 2θ, where θ is the corresponding Bragg angle. We neglected corrections for instrumental broadening in the calculation.

  The crystallinity was calculated from the areas of crystalline diffraction peaks and the amorphous area using Hinrichen's method as^[32]:

  ${C_{\rm{r}}} = {A_{\rm{c}}}/({A_{\rm{a}}} + {A_{\rm{c}}})$

  where A_c is the area of crystalline peaks and A_a is the area of amorphous peak.

  Dynamic Monte Carlo Simulations

  We performed dynamic Monte Carlo simulation to study the polymerization of PPTA. The 26214, 78644, 131072, 183502, 235930 monomers were preset in a 64 × 64 × 64 lattice box to reach the occupation density 0.1, 0.3, 0.5, 0.7, 0.9, respectively according to our previous study^[33]. Generally, each monomer occupied a single lattice site, and a chain like polymer could be mimicked by consecutive occupied sites on the cubic lattice linked with bonds. All monomers were predefined as bifunctional, containing two reactive end groups, which could form bonds by reacting with each other. Monomers underwent athermal relaxation over a long enough period to become the bulk amorphous phase, and then adopted the sampling algorithm to determine whether a new conformation could be accepted.

  In our algorithm, new configuration was obtained by both monomer movements and reactions. The movement was accomplished by the model with single-site jumping in company with periodic boundary conditions. Chain dynamics followed the relaxation algorithm that was in good accordance with both the Rouse model in dilute solutions and the reptation models in concentrated one. Double monomer occupation and bond crossing were forbidden to mimic the volume exclusion of polymer chains.

  For the reaction part, a monomer and a random neighbor site of it were chosen to check whether these two sites could be linked with a new bond. It must be noted that the selected two monomers should contain opposite reactive groups and the reaction within one molecule was forbidden. In the algorithm, the reaction probability k_MC could be employed to study the kinetics of polymerization. It is defined as the acceptance ration of reaction and directly analogous to ${{\rm{e}}^{ - {E_{\rm{a}}}/(RT)}}$. Here E_a is the activation energy, R is the gas constant, and T is temperature. According to Arrhenius equation^[34], the apparent reaction rate is k_app = A${{\rm{e}}^{ - {E_{\rm{a}}}/(RT)}}$, where A is 'pre-exponential factor' or 'frequency factor', E_a is the activation energy, R is the gas constant, and T is temperature. Thus, the reaction probability should be proportional to the apparent reaction rate k_app, and could be used to control the rate of reaction. Whether a reaction would take place or not was determined by comparing a random number r ∈ [0, 1) with reaction probability, k_MC. If r < k_MC, the reaction is allowed, otherwise, it was rejected. Time unit in our simulation is defined as one Monte Carlo cycle (we labeled as MCC in the following) for denoting as the attempted move of the total amount of monomers.

  RESULTS AND DISCUSSION

  Poly(p-phenylene terephthalamide) Synthesis

  Monomer concentration

  The monomer concentration had a great influence on η_inh of PPTA. As shown in Fig. 1, the range from 0.2 mol/L to 0.6 mol/L of monomer concentration was investigated to study the effect of monomer concentration on PPTA. The range from 0.35 mol/L to 0.45 mol/L was a good choice for the preparation of PPTA with higher molecular weight. When the monomer contraction was low, some side reactions, like the hydrolysis of TPC with trace amounts of water and oxidation of PPD with trace amounts of oxygen, would prevent the growth of molecular chains. However, when the monomer concentration was too high, it would cause an ultra-fast reaction rate so that the solubility of polymers decreased to form the gel, causing the reactive groups to be embedded in them and difficult to diffuse, which would be adverse to further polymer chain growth. It needs large energy input to mix the gelatinous or solid-state polymers. Furthermore, the ultra-fast reaction rate, caused by high monomer concentration, could also generate immense heat that gave rise to side reactions, such as branching and crosslinking. When the monomer concentration was proper, there would be an appropriate collision probability between monomers, oligomers and polymers, which was also beneficial to obtaining PPTA with high molecular weight.

  Figure 1

  

  Figure 1.  Effect of monomer concentration on η_inh (reaction conditions: c(CaCl₂) = 6.5 wt%, molar ratio (TPC:PPD) = 1.01, c(pyridine) = 0.6 mol/L, t = 60 min)

  DownLoad: Full-Size Img PowerPoint

  Reaction temperature

  The effect of reaction temperature on η_inh of PPTA is shown in Fig. 2. It can be seen that the number-average degree of polymerization increased with the increase of reaction temperature, but decreased when the temperature ranged from -5 ℃ to 15 ℃. It can also be found that the molecular weight decreased when the temperature ranged from 0 ℃ to 15 ℃. This behavior was because the polycondensation of TPC and PPD, which had low activation energy and high reaction rate constant (1000 L/(mol·s)), would generate a lot of heat (about 199 kJ)^[35] and make the reaction temperature rapidly increase about 20 ℃ in 10 s at the initial stage of reaction^[15]. The high reaction temperature and intense reaction heat would lead to premature precipitation of PPTA gel, which was unfavorable for the preparation of PPTA with high molecular weight. In addition, high reaction temperature could also lead to oxidation of PPD and the side reactions of TPC, which would not only destroy monomer molar ratio, but also increase the risk of adverse reactions, and lead to the formation of by-products. If the reaction temperature was too low, it would cause the imbalance of the reaction ratio due to the decreased solubility of monomers in solvent and also prevent obtaining high molecular weight polymers owing to the low reaction rate. As a result, the low temperature ranging from -5 ℃ to 5 ℃ was the best condition to achieve PPTA with high molecular weight.

  Figure 2

  

  Figure 2.  Effect of reaction temperature on η_inh (reaction conditions: c₀ = 0.4 mol/L, c(CaCl₂) = 6.5 wt%, molar ratio (TPC:PPD) = 1.01, c(pyridine) = 0.6 mol/L, t = 60 min)

  DownLoad: Full-Size Img PowerPoint

  Reaction time

  Figure 3 presents the effect of reaction time on η_inh and ${\bar X_{\rm{n}}} $ of PPTA. As shown in Fig. 3, the η_inh of PPTA grew to 1.3 dL/g in less than 5 min due to the ultra-fast reaction of PPD and TPC. Then the inherent viscosity of PPTA continued to increase rapidly until 40 min and then slowed down until it got close to a limit value. This was primarily due to the reaction system which was still in the homogeneous solution state at the beginning of polymerization. Masses of amino groups and acyl chloride groups were full of the reaction system to react with high collision probability because of the lower molecular weight and lower viscosity of systems. The reaction rate was ultra-fast. After the η_inh reached 5.1 dL/g, the residual concentrations of amino groups and acyl chloride groups were quite low compared to the initial concentration. The increasing viscosity made the oligomers difficult to transfer. What was worse, some reactive groups might be embedded in the precipitating solid state and lost their activity. This made the reaction rate decrease and the η_inh tended to be stable after 50 min. Another possible reason for the reduction of rate at the later stage was that the side reaction became comparable to the primary reaction rate. Thus, the end groups on small or large molecules were consumed with equal probability by the side reaction, reducing the biased consumption of oligomers by the diffusion-controlled primary reaction. Therefore, 50 min might be a good choice for the reaction time. Whatever, it is an important guarantee for reducing the reaction rate by strictly controlling the reaction temperature before 30 min.

  Figure 3

  

  Figure 3.  Effect of reaction time on η_inh (reaction conditions: c₀ = 0.4 mol/L, c(CaCl₂) = 6.5 wt%, molar ratio (TPC:PPD) = 1.01, c(pyridine) = 0.6 mol/L)

  DownLoad: Full-Size Img PowerPoint

  Microstructure of the prepared PPTA by X-ray diffraction

  Based on the optimal conditions as mentioned above, PPTA samples with different inherent viscosities were obtained by the twin screw. The detailed technological parameters for each reaction step within the twin screw will be discussed in another article. In the present study, microstructure parameters of the prepared PPTA resin were investigated by X-ray diffraction technique. An X-ray beam directed perpendicularly to the axis produced reflections from layer planes. The Scherrer equation was used to calculate the stacking height of layer planes in vertical direction of the crystal. Figure 4 presents equatorial X-ray diffraction patterns of PPTA with different inherent viscosities recorded at room temperature. Qualitative inspection of equatorial X-ray diffraction patterns showed three sharp peaks at about 2θ =20.9° (d = 0.42 nm), 2θ = 23.6° (d = 0.39 nm) and 2θ = 28.5° (d = 0.31 nm), which could be indexed as (110), (200) and (004) diffractions, respectively^{[36, 37]}. Crystal parameters obtained from equatorial X-ray diffraction patterns are given in Table 1. It indicates that the crystallinity increased with the inherent viscosity but the stacking size (D) of PPTA was almost invariable even with different inherent viscosities and crystallinities.

  Figure 4

  

  Figure 4.  X-ray powder diffraction patterns of PPTA recorded at room temperature

  DownLoad: Full-Size Img PowerPoint

  Table 1

  

  Table 1.  Crystal parameters of PPTA with different inherent viscosities

  DownLoad: CSV

  ηinh (dL/g)	Crystallinity (%)	(110)			(200)			(004)
  		2q (°)	D (Å)		2q (°)	D (Å)		2q (°)	D (Å)
  4.5	48.69	20.6	32		23.0	30		28.3	23
  5.2	51.53	20.7	28		23.1	29		28.5	20
  6.4	54.53	20.6	29		23.0	31		28.2	23
  7.6	57.40	20.6	31		22.9	27		28.4	24
  8.1	59.75	20.9	30		23.2	26		28.4	21

  Kinetics of PPD/TPC Polycondensation

  To better understand the kinetics of polycondensation for preparing PPTA, a kinetics model in this work was built based on our previous work^[33]. In this model, the reaction probability k_MC, which is defined as the acceptable ration of reaction, was employed to study the kinetics of polymerization. It would be proportional to the apparent reaction rate k_app, and could be used to control the rate of reaction.

  In the early stage of polycondensation, viscosity of the reaction system was not very high which assured the free movement of molecules in the system. The reaction between amine groups and acyl chloride groups strictly obeyed the second order reaction kinetics, where the molecular weight increased linearly with the progress of polymerization. However, when the reaction probability increased, the number-average degree of polymerization (${\bar X_{\rm{n}}}$) will not be proportional to reaction time. That is because the molecular weight of the final polymer is dependent on factors such as the reaction temperature, stirring rate, solvent composition, stoichiometry and ingredients concentration. Bair et al.^[21] gave a general schematic representation of the polymerization of PPTA that an initial rapid increase of molecular weight and transient stir-opalescence was followed by gelation and subsequent retardation of the polymerization rate. They also found that the polymer inherent viscosity could lead to the change of the effective axial ratio of polymer chains by changing the average degree of polymerization or chain-to-chain association and eventually alter the critical concentration of anisotropic phase and affect the reaction rate. Gupta et al.^[22] also observed this deviation phenomenon in the experimental studies of the kinetics of solution polymerization to synthesize PPTA. The process showed a typical behavior of a diffusion-controlled step-growth polymerization that the degree of polymerization increased slowly after an initial period of rapid increase. Only in the very early stage, the degree of polymerization increased linearly with time with the slope proportional to the rate constant and the initial monomer concentration, which is so called the second order reaction kinetics. It has been observed that there was a transition point of reaction time (t) which represented the transition from the reaction-controlled regime to the diffusion-controlled regime. During the reaction-controlled regime, the slope obeyed the second order reaction kinetics that was clearly studied by Flory^[13]. Further, for the diffusion-controlled regime, our previous work^[33] has already provided a good description of kinetics using the Rouse scaling. Similarly, for PPTA, the rod-like rigid polymers, the diffusion coefficient has the scaling of $ D\sim {({\bar X_{\rm{n}}})^{ - 2}}c_0^{ - 3}$ at semidilute solution with entanglements according to the reptation model^[38]. Thus, with the similar deduction method mentioned in our previous work^[33], the scaling exponent between $ {\bar X_{\rm{n}}} $, c₀ and t should be

  ${\bar X_{\rm{n}}} \sim c_0^{ - 0.88} \cdot {t^{0.37}}$

  Thus the number-average degree of polymerization ($ {\bar X_{\rm{n}}} $) could be calculated by Eq. (10) with knowing the monomer concentration (c₀) and reaction time (t). Experimental results from the current work in Figs. 1 and 3 are also shown in Fig. 5 by logarithm transformation.

  Figure 5

  

  Figure 5.  (a) Variation of $ {\bar X_{\rm{n}}} $ of PPTA with monomer concentration (c₀); (b) Variation of $ {\bar X_{\rm{n}}} $ of PPTA with reaction time (All data points of $ {\bar X_{\rm{n}}} $ here were firstly obtained by transforming the experimental data of Figs. 1 and 3 using Eqs. (2)-(6), followed by a logarithmic transformation. The red lines were drawn to guide the eyes.)

  DownLoad: Full-Size Img PowerPoint

  As shown in Fig. 5(a), the solution polymerization was investigated from the $ {\bar X_{\rm{n}}} $ obtained at the same reaction time but at various monomer concentrations. It can be seen that the scaling of concentration dependence showed two regimes. When c₀ < 0.4 mol/L, the number-average molecular weight bordered on linear increasing with c₀. However, it can be seen that the $ {\bar X_{\rm{n}}} $ increased dramatically with the increase of the initial monomer concentration at 0.3 mol/L < c₀ < 0.4 mol/L but decreased rapidly at c₀ > 0.4 mol/L which was affected by diffusion. Although the polymerization of PPTA kept the diffusion-controlled mechanism of stepwise polymerization, the most important feature of this process was that the polymerization could be realized by the parallelly arranged oligomers. PPTA would be obtained with reaction-controlled kinetics in dilute solution having mutual influence and interaction between molecules should be ignored. All the molecules were treated as particles in a hydrodynamic continuum that the diffusion coefficients were calculated in terms of the rod length, length to cross-sectional diameter ratio and solvent viscosity. Therefore, the scaling exponent of this regime was 1.12 that is in good accordance with the feature of second-order reaction kinetics, as shown in Fig. 5(a). Narrow gap between theoretical value (slope = 1.0) and experimental results (slope = 1.12) may be due to the effect of cosolvent used to weaken the interaction between molecular chains and promote their diffusion.

  With the increasing monomer concentration, a diffusion constant strongly dependent on chain length altered this situation. The chain lengths increased longer in higher concentration so that their rotational diffusion constants asymptotically approached zero. The time required to form the transition state necessary for condensation was longer than the lifetime for reaction. The rate-limiting step would be the formation of collinear alignment transition state. In the extreme, all molecules achieved co-linearity and proximity condense by diffusion and the polymerization rate was controlled by the rate at which this transition state was formed. Furthermore, a similarly definitive analysis about reaction or diffusion by reaction rate theory of relating the reaction probability to the time has been given in our previous study. It could be found that the scaling of concentration rapidly decreased because the entanglements restricted the diffusion within a primitive tube. The scaling exponent between $ {\bar X_{\rm{n}}} $ and c₀ in our previous study would be -1.8 when c₀ > 0.7 with flexible chains. However, for the rod-like molecular, this similar scaling exponent for decreasing had been easily achieved when c₀ > 0.4 mol/L. As shown in Fig. 5(a), the scaling of concentration dependence was close to the scaling in Eq. (10). The gap between the theoretical value (slope = -0.88) and experimental results (slope = -1.1) may be due to the self-diffusion coefficient (D), which was used to describe the rod-like polymers with part flexible segment. But the diffusion of rod-like molecules was more difficult than the flexible chains in semi-dilute solutions. Therefore, the scaling exponent in our simulation results showed that the molecular weight was more obviously affected by the concentration. It may also be noted that time for diffusion was merely comparable with time for reaction and strongly dependent on the chain length. Although these conditions did not apply to flexible chain polymers, the severely decreased mobility of the rod-like chains appeared to foster conditions under which condensation proceeded through a mechanism that could not only be modelled by the equilibrium stepwise polymerization.

  With the double logarithmic plots of $ {\bar X_{\rm{n}}} $ versus t as shown in Fig. 5(b), we observed two regimes. One was the reaction-controlled at the early stage of polymerization (t < 15 min) with the slope of 1.19, and the other was the diffusion-controlled at the later stage (t > 30 min) with the slope of 0.35. This scaling indicated from experimental results demonstrated a good agreement with the theoretical analysis of Eq. (10). It is also clear to see that the $ {\bar X_{\rm{n}}} $ remained unchanged after t > 50 min.

  Further examination of the polycondensation process was carried out with the $ {\bar X_{\rm{n}}} $ obtained at the same simulation time but at various concentrations and reaction probability k_MC, as shown in Fig. 6. It can be observed that the maximum degree of polymerization was obtained when the concentration of the reactants was 0.5 mol/L under the small reaction probability k_MC = 0.05 and 0.1. The degree of polymerization increased linearly with increasing c₀ under lower reaction probability (k_MC = 0.001, 0.005 and 0.01) because of the reaction-controlled effect. The possible explanation for the drop-off of degree of polymerization at higher reactant concentration and higher reaction probability was that the reactant mobility reduced before high molecular weight could be reached. This decreased diffusion ability of polymer chains led to the lower collision probability of the end groups. With higher reaction probability (k_MC ≥ 0.3), it can be seen that the $ {\bar X_{\rm{n}}} $ decreased gradually with increasing c₀ and the increasing extent of $ {\bar X_{\rm{n}}} $ at the same monomer concentration but different reaction probability also decreased. In the extreme, the $ {\bar X_{\rm{n}}} $ obtained at c₀ = 0.9 mol/L and different reaction probability (k_MC = 0.5, 0.7 and 1.0) almost merged with each other, indicating that effect of k_MC was insignificant and the reaction kinetics was dominantly controlled by diffusion as a result of the lower diffusion coefficient at high concentration and high reaction probability. Similar results were observed in the other experimental researches. Wang et al.^[39] proposed a new approach for the preparation of PPTA. A medium monomer concentration range (0.3 mol/L to 0.4 mol/L) will certainly do favor to form PPTA with high molecular weight. Bair et al.^[21] also studied the polymerization in HMPA/NMP solution and obtained the maximum η_inh when the concentration centration of the reactants was 0.25 mol/L. They concluded that the possible reason for the drop-off of η_inh at higher reactant concentration was a combination of both the reduced reactant mobility due to the early-reached onset of gelation and an increase in the rate of side reactions as a result of great heat generation. The effect of side reaction on molecular weight has been studied by Gupta et al^[22]. Their results showed that in the case of no side reaction there was a monotonic increase in the finial degree of polymerization with a change in the initial monomer concentration, even though there was an approach to an asymptotic value at higher concentrations. However, in the case with side reactions, the maximum at a particular concentration was observed because an increase in monomer concentrations would result in the higher rate of side reactions, and consequently a lower molecular weight. The calculations indicated that the effects of diffusion control as well as side reaction may be responsible for the experimentally observed optimal monomer concentration.

  Figure 6

  

  Figure 6.  The plots of $ {\bar X_{\rm{n}}} $ versus c₀ with different small reaction rates (k_MC = 0.001, 0.005, 0.01, 0.05, 0.1, 0.3, 0.4, 0.5, 0.7, 1.0. All the results were recorded at the same time (t = 5 × 10⁵ MCC). The solid lines were drawn to guide the eyes.)

  DownLoad: Full-Size Img PowerPoint

  CONCLUSIONS

  In this work, the polycondensation reaction between p-phenylenediamine (PPD) and terephthaloyl chloride (TPC) was performed to synthesize poly(p-phenylene terephthalamide) (PPTA). Effects of a number of factors, including monomer concentration, reaction temperature and reaction time on the molecular weight of PPTA were investigated to determine the optimum conditions for preparing high molecular weight PPTA. Furthermore, we studied the kinetics of polycondensation with theoretical analysis and dynamic Monte Carlo simulation. The theoretical results for the variation of the degree of polymerization with time showed a typical behavior of a diffusion-controlled stepwise polymerization with severe slowing of the reaction at the later stages. The simulation result showed the number-average degree of polymerization to be of the form ${\bar X_{\rm{n}}} \sim c_0^{ - 0.88} \cdot {t^{0.37}}$, which could be used to predict the polycondensation process with monomer concentration and reaction time. By comparing the theoretical value and experimental data, we concluded that the diffusion-controlled effect had a more significant impact on the polymerization of PPTA. The number-average degree of polymerization showed more severe effect by the monomer concentration, but less by reaction time. The computations also showed the existence of an optimal initial monomer concentration at which the degree of polymerization at a fixed time of reaction was the maximum. The theoretical model showed a good agreement with the experimental results of the polycondensation process and provided a quantitative description of the diffusion-controlled polymerization of PPTA to some extent.

• 1. [1]

     Rao Y., Waddon A., Farris R.. Structure-property relation in poly(p-phenylene terephthalamide) (PPTA) fibers[J]. Polymer, 2001, 42(13):  5937-5946. doi: 10.1016/S0032-3861(00)00905-8

  2. [2]

     Mark H., Atlas S., Ogata N.. Aromatic polyamide[J]. J. Polym. Sci., 1962, 61(172):  49-53. doi: 10.1002/pol.1962.1206117225

  3. [3]

     Anagnostopoulos G., Parthenios J., Galiotis C.. Thermal stress development in fibrous composites[J]. Mater. Lett., 2008, 62(3):  341-345. doi: 10.1016/j.matlet.2007.05.031

  4. [4]

     Knijnenberg A., Bos J., Dingemans T. J.. The synthesis and characterisation of reactive poly(p-phenylene terephthalamide)s:a route towards compression stable aramid fibres[J]. Polymer, 2010, 51(9):  1887-1897. doi: 10.1016/j.polymer.2010.03.015

  5. [5]

     Rao Y., Waddon A., Farris R.. The evolution of structure and properties in poly(p-phenylene terephthalamide) fibers[J]. Polymer, 2001, 42(13):  5925-5935. doi: 10.1016/S0032-3861(00)00906-X

  6. [6]

     Du S., Wang W., Yan Y., Zhang J., Tian M., Zhang L., Wan X.. A facile synthetic route to poly(p-phenylene terephthalamide) with dual functional groups[J]. Chem. Commun., 2014, 50(69):  9929-9931. doi: 10.1039/C4CC02366H

  7. [7]

     Du S., Zhang J., Guan Y., Wan X.. Sequence effects on properties of the poly(p-phenylene terephthalamide)-based macroinitiators and their comb-like copolymers grafted by polystyrene side chains[J]. Aust. J. Chem., 2014, 67(1):  39-48. doi: 10.1071/CH13291

  8. [8]

     Schwartz P.. A review of recent experimental results concerning the strength and time dependent behavior of fibrous poly(paraphenylene terephthalamide)[J]. Polym. Eng. Sci., 1987, 27(11):  842-847. doi: 10.1002/(ISSN)1548-2634

  9. [9]

     Perepelkin K. E., Machalaba N. N.. Recent achievements in structure ordering and control of properties of para-aramide fibres[J]. Mol. Cryst. Liq. Cryst., 2000, 353(1):  275-286. doi: 10.1080/10587250008025667

  10. [10]

      Sun L., Xu J., Luo W., Guo C., Tuo X., Wang X.. Investigation on the preparation of high molecular weight poly(p-phenylene terephthalamide) using CaH₂ as acid absorbent[J]. Acta Polymerica Sinica (in Chinese), 2012, (1):  70-74.

  11. [11]

      Wang S., Liu H., Xiao R.. Determination of condensation-polymerization thermal effect of poly(paraphenylenetere-phalamide)[J]. Journal of DongHua University (in Chinese)., 1984, 1:  41-46.

  12. [12]

      Chae H. G., Kumar S.. Rigid-rod polymeric fibers[J]. J. Appl. Polym. Sci., 2006, 100(1):  791-802. doi: 10.1002/(ISSN)1097-4628

  13. [13]

      Flory, P. J., Principles of polymer chemistry, Cornell University Press, New York, 1953, p. 317.

  14. [14]

      Cotts D. B., Berry G. C.. Polymerization kinetics of rigid rodlike molecules:polycondensation of poly([benzo (1, 2-d:5, 4-d') bisoxazole-2, 6-diyl]-1, 4-phenylene)[J]. Macromolecyles, 1981, 14(4):  930-934. doi: 10.1021/ma50005a008

  15. [15]

      Agarwal U., Khakhar D.. Enhancement of polymerization rates for rigid rod-like molecules by shearing[J]. Nature, 1992, 360:  53-55. doi: 10.1038/360053a0

  16. [16]

      Agarwal U., Khakhar D.. Diffusion-limited polymerization of rigid rodlike molecules:dilute solutions[J]. J. Chem. Phys., 1992, 96(9):  7125-7134. doi: 10.1063/1.462546

  17. [17]

      Agarwal U., Khakhar D.. Shear flow induced orientation development during homogeneous solution polymerization of rigid rodlike molecules[J]. Macromolecules, 1993, 26(15):  3960-3965. doi: 10.1021/ma00067a035

  18. [18]

      Agarwal U., Khakhar D.. Simulation of diffusion-limited step-growth polymerization in 2D:effect of shear flow and chain rigidity[J]. J. Chem. Phys., 1993, 99(4):  3067-3074. doi: 10.1063/1.466195

  19. [19]

      Agarwal U., Khakhar D.. Diffusion-limited polymerization of rigid rodlike molecules:semidilute solutions[J]. J. Chem. Phys., 1993, 99(2):  1382-1392. doi: 10.1063/1.465382

  20. [20]

      Arpin M., Strazielle C.. Characterization and conformation of aromatic polyamides:poly(1, 4-phenylene terephthalamide) and poly(p-benzamide) in sulphuric acid[J]. Polymer, 1977, 18(6):  591-598. doi: 10.1016/0032-3861(77)90061-1

  21. [21]

      Bair T., Morgan P., Killian F.. Poly(1, 4-phenylenetere-phthalamides). polymerization and novel liquid-crystalline solutions[J]. Macromolecules, 1977, 10(6):  1396-1400. doi: 10.1021/ma60060a042

  22. [22]

      Gupta J. S., Agge A., Khakhar D.. Polymerization kinetics of rodlike molecules under quiescent conditions[J]. AlChE J., 2001, 47(1):  177-186. doi: 10.1002/(ISSN)1547-5905

  23. [23]

      Bao J. S., You A. J., Zhang S. Q., Zhang S. A., Hu C.. Studies on the semirigid chain polyamide-poly(1, 4-phenylenetere-phthalamide)[J]. J. Appl. Polym. Sci., 1981, 26(4):  1211-1220. doi: 10.1002/app.1981.070260413

  24. [24]

      Doi, M. ; Edwards, S. F., The theory of polymer dynamics, Oxford University Press, New York, 1988, p. 295.

  25. [25]

      Tracy M., Pecora R.. Dynamics of rigid and semirigid rodlike polymers[J]. Annu. Rev. Phys. Chem., 1992, 43(1):  525-557. doi: 10.1146/annurev.pc.43.100192.002521

  26. [26]

      Doi M.. Molecular dynamics and rheological properties of concentrated solutions of rodlike polymers in isotropic and liquid crystalline phases[J]. J. Polym. Sci., Part B, 1981, 19:  229-243.

  27. [27]

      Teraoka I., Hayakawa R.. Theory of dynamics of entangled rod-like polymers by use of a mean-field green function formulation.Ⅰ. transverse diffusion[J]. J. Chem. Phys., 1988, 89(11):  6989-6995. doi: 10.1063/1.455325

  28. [28]

      Teraoka I., Hayakawa R.. Theory of dynamics of entangled rod-like polymers by use of a mean-field green function formulation.Ⅱ. rotational diffusion[J]. J. Chem. Phys., 1989, 91(4):  2643-2648. doi: 10.1063/1.456973

  29. [29]

      Agge A., Jain S., Khakhar D.. Acceleration of the polymerization of rodlike molecules by flow[J]. J. Am. Chem. Soc., 2000, 122(44):  10910-10913. doi: 10.1021/ja001541r

  30. [30]

      Jain S., Agge A., Khakhar D.. Flow enhanced diffusion-limited polymerization of rodlike molecules[J]. J. Chem. Phys., 2001, 114(1):  553-560. doi: 10.1063/1.1330211

  31. [31]

      Zhang R., Kong H. J., Zhong H. P., Liu J., Zhou J. J., Teng C. Q., Ma Y., Yu M. H.. N-Alkyl PPTA:preparation and characterization[J]. Adv. Mater. Res., 2012, 554:  105-109.

  32. [32]

      Fitzer E., Müller D.. The influence of oxygen on the chemical reactions during stabilization of pan as carbon fiber precursor[J]. Carbon, 1975, 13(1):  63-69. doi: 10.1016/0008-6223(75)90259-6

  33. [33]

      Liu J., Ma Y., Wu R., Yu M.. Molecular simulation of diffusion-controlled kinetics in stepwise polymerization[J]. Polymer, 2016, 97:  335-345. doi: 10.1016/j.polymer.2016.05.050

  34. [34]

      Atkins, P. ; Paula, D. J. Physical Chemistry, W. H. Freeman & Company, New York, 2006, p. 807.

  35. [35]

      Wang S., Liu H., Xiao R.. Determination of condensation-polymerization thermal effect of poly(paraphenylenetere-phalamide)[J]. Journal of DongHua. University, 1984, 1:  41-46.

  36. [36]

      Northolt M.. X-ray diffraction study of poly(p-phenylene terephthalamide) fibres[J]. Eur. Polym. J., 1974, 10(9):  799-804. doi: 10.1016/0014-3057(74)90131-1

  37. [37]

      Northolt M., van Aartsen J.. On the crystal and molecular structure of poly-(p-phenylene terephthalamide)[J]. J. Polym. Sci., Part C:Polym. Lett., 1973, 11(5):  333-337. doi: 10.1002/pol.1973.130110508

  38. [38]

      Bu Z., Russo P. S., Tipton D. L., Negulescu I. I.. Self-diffusion of rodlike polymers in isotropic solutions[J]. Macromolecules, 1994, 27(23):  6871-6882. doi: 10.1021/ma00101a027

  39. [39]

      Wang P., Wang K., Zhang J.. Non-aqueous suspension polycondensation in NMP-CaCl₂/paraffin system-A new approach for the preparation of poly(p-phenylene terephthalamide)[J]. Chinese J. Polym. Sci., 2015, 33(4):  564-575. doi: 10.1007/s10118-015-1607-1

•