polymers Article
Effect of Moisture on Mechanical Properties and Thermal Stability of Meta-Aramid Fiber Used in Insulating Paper Fei Yin 1 , Chao Tang 1,2, *, Xu Li 1 and Xiaobo Wang 1 1 2
*
College of Engineering and Technology, Southwest University, Chongqing 400715, China;
[email protected] (F.Y.);
[email protected] (X.L.);
[email protected] (X.W.) School of Electronics and Computer Science, University of Southampton, SO171BJ Southampton, UK Correspondence:
[email protected]; Tel.: +86-23-6825-1265
Received: 19 September 2017; Accepted: 18 October 2017; Published: 22 October 2017
Abstract: Seven composite models of meta-aramid fibers with different moisture contents were studied using molecular dynamics simulation. The effects of moisture on the thermal stability and mechanical properties of the fibers and their mechanisms were analyzed, considering characteristics such as hydrogen bonding, free volume, mean square displacement, and mechanical parameters. The simulation results showed that the large number of hydrogen bonds between water molecules and meta-aramid fibers destroyed the original hydrogen-bond network. Hydrogen bonds between the molecular chains of meta-aramid fibers were first destroyed, and their number decreased with increasing moisture content. The free volume of the fibers thereby increased, the interactions between fiber chains weakened with increasing moisture content, and the fiber chain movement intensified accordingly. The ratio of diffusion coefficients of the water molecules to moisture contents of the composite models increased linearly, and the water molecule diffusion increased, which accelerated the rate of damage to the original hydrogen-bond network of the meta-aramid fibers and further reduced their thermal stability. In general, the mechanical properties of the composites were negatively related to their moisture content. Keywords: meta-aramid fibers; moisture; hydrogen bond; mean square displacement; free volume
1. Introduction Oil-paper systems comprise the main insulation structures of oil-immersed power transformers. In long-term operation of a transformer, the insulating oil will decompose to produce water. Moisture accelerates aging of the insulating paper and decreases its mechanical, thermal stability, and dielectric properties [1,2]. During long-term operation of oil-paper transformer insulation systems, the moisture content of the paper will gradually increase to a certain value and eventually reach equilibrium with the moisture in the transformer oil. One of the main degradation products of paper is cellulose. Moisture increases the probability of fracture of the cellulose molecular chains under combined action with other degradation products [3–5]. Simultaneously, a large number of water molecules can form space bubbles at high temperature, which further deteriorate the properties of the insulating paper. The effect of moisture is also reflected in the reduction of the degree of polymerization of these large polymers, in the acceleration of the aging process of the insulating paper, and in the quantity of hydrogen ions in the paper. A hydrolytic catalyst is produced by these ions, which will accelerate cellulose hydrolysis. In this respect, studies have shown that a doubling of the moisture content causes a 50% decrease in the mechanical properties of insulating paper [6,7]. Numerous studies that have been conducted on the mechanical and electrical properties of transformer insulation systems indicate that moisture is one of the most important factors affecting transformer performance [8–10]. Polymers 2017, 9, 537; doi:10.3390/polym9100537
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Aromatic polyamide macromolecules are high-performance materials that have been widely used in oil-paper insulating systems. A large amount of research by Chinese scholars on the thermal degradation of aramid fibers has shown that these fibers have high heat resistance, a service life exceeding 10 years at 180 ◦ C, and good mechanical properties that are maintained at temperatures up to 300 ◦ C [11,12]. Although aramid fibers have excellent performance, their mechanical properties deteriorate under conditions of long-term use that may imply thermal aging, surface damage, and cracking. Research of Jain, A. et al. [13] on thermal aging of Nomex fiber showed that temperature and time of exposure to air were the main factors influencing fiber's thermal degradation. Villar-Rodil, S. et al. studied the pyrolysis behavior of Nomex aramid fiber and the properties of the thermal degradation product. They showed that quality loss due to thermal aging of the fiber was divided into three stages [14]. Improvements in industrial technology have led to improved chromaticity, light resistance, and fatigue resistance of meta-aramid fibers. Numerous studies show that the properties of high molecular mass polymers [15–19] can be effectively improved by adopting technologies such as nanometer modification and grafting. Zhao, L.H. et al. [20] combined the aramid fiber with other materials. Chen, L. et al. [21] modified the aramid fiber by low-temperature solution copolymerization, which improved the service life, heat resistance, and mechanical properties of the resulting composite paper. Bai, G. et al. [22] effectively lowered the conductive current of the aramid fiber and improved the alternating-current (AC) breakdown field by modifying 1313 fibers with nanometer silicon nitride. By using grafting, Wang, H.H. et al. [23] increased the stretching, bending, and impact strengths of a composite material of the aramid fiber by 19.1%, 49.3%, and 46.8%, respectively. Current studies on aramid fibers mainly focus on the macroscopic processes of thermal aging and physical and chemical modification; however, the micromechanistic effect on the mechanical properties of these fibers is rarely reported, despite moisture being an important factor affecting the performance of transformer oil-paper insulating systems. Most studies of the aramid fiber have been conducted from the macroscopic point of view, but the mechanism of the effect of moisture on aramid fiber properties cannot be analyzed from the macroscopic angle. Using molecular dynamics (MD), a cost-effective scientific tool, the property changes of a substance and their microscopic mechanisms [24–29] can be studied at the molecular and atomic levels. In this work, the effect of moisture on the properties of meta-aramid fiber insulating paper was studied using MD to explore the micromechanism. Seven models of meta-aramid fibers with different moisture contents were constructed, and dynamic simulation of each was carried out using Materials Studio software (Accelrys, San Diego, CA, USA). Variations in mechanical properties and thermal stabilities of the mixed models, performance parameters of the hydrogen bonding, as well as the related mechanisms were analyzed. 2. Model Calculation and Parameter Analysis 2.1. Modeling In long-term operation of an oil-immersed transformer, the moisture content of the insulating paper may increase to 5% [17,30], or even higher in extreme cases. Considering that meta-aramid fibers have excellent structural stability and high temperature resistance, appropriate moisture contents were selected for comparison. Meta-aramid-H2 O composite models with moisture contents of 0%, 1%, 2%, 3%, 4%, 5% and 9% were constructed; to facilitate description, these models are respectively marked as P_W0 , P_W1 , P_W2 , P_W3 , P_W4 , P_W5 , and P_W9 . The Visualizer module in the Materials Studio software package was first used to construct meta-aramid fibers with a degree of polymerization of 20. The water molecule model was then constructed, and, finally, the composite models were built using the Amorphous Cell module. To eliminate boundary effects and maintain a constant system density, a periodic boundary condition was adopted, with the density set at 1.4 g/cm3 [31].
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boundary effects and maintain a constant system density, a periodic boundary condition was adopted, with the density set at 1.4 g/cm3 [31]. Considering Considering the the situation situation in in which which the the motion motion of of water water molecules molecules is is random random when when the the moisture moisture content is low, the water-free model (P_W ) and the composite model with a moisture content of 4% 4% content is low, the water-free model (P_W00) and the composite model with a moisture content of (P_W as the and comparison models. Considering the temperature (P_W44)) were wereadopted adopted as study the study and comparison models. Considering the environment temperature of a transformer oil-paper insulation system, the simulated temperatures were set at 343, 363, 383, environment of a transformer oil-paper insulation system, the simulated temperatures were set403 at and 423 K for the study of the effect of temperature on the mechanical properties of the meta-aramid 343, 363, 383, 403 and 423 K for the study of the effect of temperature on the mechanical properties of fibers. The P_W0fibers. , P_W1The , P_W P_W shown in Figure 1a–d 4 and 9 models the meta-aramid P_W 0, P_W 1, P_W 4 and are P_W 9 models are shown inrespectively. Figure 1a–d respectively.
Figure1.1.(a) (a)P_W P_W00;, (b) (b) P_W P_W11;, (c) (c) P_W P_W44 and Figure and (d) (d) P_W P_W99models modelsof ofmeta-aramid meta-aramidfiber fibermolecules. molecules.
2.2. Molecular Molecular Dynamics Dynamics Analog Analog Calculation Calculation 2.2. Energy minimization minimization (Minimizer) (Minimizer) of the constructed constructed composite composite models models was was carried carried out out using using Energy of the the Discover module to ensure that the energy of each constructed system was in the lowest the Discover module to ensure that the energy of each constructed system was in the lowest state. state. Smart Minimizer Minimizer was was adopted adopted for for the the energy energy minimization, minimization, the the convergence convergence level level was was selected selected as as Smart Medium, and and the the maximum maximum number number of of iterations iterations was was set set at at 5000. 5000. When more stable stable model model was was Medium, When aa more obtained, annealing treatment of the system was carried out using the Forcite module. Annealing obtained, annealing treatment of the system was carried out using the Forcite module. Annealing was was carried out four consecutive at a temperature the range The systems carried out four consecutive timestimes at a temperature in theinrange of 300ofto300 900toK.900 TheK.systems were were then considered to be at thermodynamic equilibrium. then considered to be at thermodynamic equilibrium. The MD MD simulations simulations were were carried carried out The out after after attaining attaining thermodynamic thermodynamic equilibrium equilibrium of of the the system. system. A 100 ps dynamic simulation was first carried out using the NVT (a certain particle number A 100 ps dynamic simulation was first carried out using the NVT (a certain particle number N, N, volume V, V, and and temperature temperature T) T) ensemble, ensemble, and and then then aa 100 was performed using volume 100 ps ps dynamic dynamic simulation simulation was performed using
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the NPT (a certain particle number N, pressure P, and temperature T) ensemble. The time step of the the NPT (a certain particle number N, pressure P, and temperature T) ensemble. The time step of the simulations was 1 fs. simulations was 1 fs. Both organic and inorganic components were involved in the model systems, so the condensedBoth organicmolecular and inorganic components were involved in the model systems, so [32], the phase optimized potentials for atomistic simulation studies (COMPASS) force field condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force which is suitable for handling such systems, was selected. The Andersen thermostat and Berendsen field [32],were whichadopted is suitable such systems, was selected. The Andersen thermostat barostat in for thehandling MD simulation. The Maxwell distribution was adopted for and the Berendsen barostat were adopted in the MD simulation. The Maxwell distribution was adopted for distribution of the initial velocity of a molecule, and the velocity Verlet leapfrog integral method was the distribution of the initial velocity of a molecule, and the velocity Verlet leapfrog integral method adopted for the solution of Newton equations. The atom-based method was used for determining the was forand the Coulomb solution offorces, Newton atom-based was[33]. used for determining Van adopted der Waals andequations. the cut-offThe radius was set method at 0.95 nm the Van der Waals and Coulomb forces, and the cut-off radius was set at 0.95 nm [33].
360
358 K
320
328 K
7000
(a)
(b)
6000
280
Temperature
Enengy (kcal/mol)
Temperature (K)
2.3. Rationality of Parameter Settings 2.3. Rationality of Parameter Settings Selection of the integration step and simulation time plays a critical role in the overall simulation Selection of the integration step and simulation time plays a critical role in the overall simulation experiment: an excessively long integration step will cause intense collisions between molecules, experiment: an excessively long integration step will cause intense collisions between molecules, which which makes the system data overflow, whereas the ability to search phase space is reduced by an makes the system data overflow, whereas the ability to search phase space is reduced by an excessively excessively short integration step. In addition, if the simulation time is too short, the simulation may short integration step. In addition, if the simulation time is too short, the simulation may end before end before reaching thermodynamic equilibrium, whereas excessively long simulation times will reaching thermodynamic equilibrium, whereas excessively long simulation times will inevitably lead inevitably lead to a waste of time. Two criteria were used for judging when a system had reached to a waste of time. Two criteria were used for judging when a system had reached equilibrium: first, equilibrium: first, the temperature reached a balanced state (i.e., the standard deviation of the temperature reached a balanced state (i.e., the standard deviation of temperature was within 15 K); temperature was within 15 K); second, the energy achieved a balanced state (i.e., the energy second, the energy achieved a balanced state (i.e., the energy fluctuated [34] above and below a certain fluctuated [34] above and below a certain fixed value). Taking the P_W4 composite model in a 343 K fixed value). Taking the P_W4 composite model in a 343 K simulated environment as an example, simulated environment as an example, Figure 2a,b indicate the temperature-time and energy-time Figure 2a,b indicate the temperature-time and energy-time variations, respectively. variations, respectively.
343 K
240
5000 4000 3000 2000 1000
Potential energy Non-bond energy
0
200
Kinetic energy Total energy
-1000
160 0
10
20
30
40 50 60 Time (ps)
70
80
90 100
0
10
20
30
40 50 60 Time (ps)
70
80
90 100
Figure system stability. Variations of (a)oftemperature and (b) energies of mixed Figure 2. 2. Basis Basisfor forjudgment judgmentofof system stability. Variations (a) temperature and (b) energies of models with time. mixed models with time.
Figure 2 shows shows that the the temperature temperature of the the whole whole system system quickly quickly reached reached aa stable stable equilibrium equilibrium non-bonding energy quickly reached a balanced balanced state state state: potential potential energy, kinetic energy, and non-bonding without violent violentoscillations, oscillations,which whichindicated indicatedthat thatthe theselection selectionofof parameters time step, total time without parameters of of time step, total time of of simulation, and other parameters were reasonable. simulation, and other parameters were reasonable. 3. Results and Discussion It is known from elastic mechanics that all mechanical parameters of a solid material can be It is known from elastic mechanics that all mechanical parameters of a solid material can be theoretically calculated from the generalized Hooke’s Law matrix, and the mechanical properties of an theoretically calculated from the generalized Hooke’s Law matrix, and the mechanical properties of object can be mainly described by the volume modulus (K), shear modulus (G), tensile modulus (E), an object can be mainly described by the volume modulus (K), shear modulus (G), tensile modulus and Cauchy pressure (C12 –C44 ). There are two ways to define a hydrogen bond: the energy criterion and (E), and Cauchy pressure (C12–C44). There are two ways to define a hydrogen bond: the energy the geometric criterion. Geometric criteria have a relatively high degree of recognition, so geometric criterion and the geometric criterion. Geometric criteria have a relatively high degree of recognition, criteria were selected to calculate hydrogen bonds in this paper. The geometric criteria of hydrogen so geometric criteria were selected to calculate hydrogen bonds in this paper. The geometric criteria
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Polymers 2017, 9, 537 14 of hydrogen bond (X–H· ··Y) are shown in Figure 3. In this paper, the distance parameter5Rof was set to 3 Å, and thebond angle(X–H· β was toshown 120°. Hydrogen is a weak interaction force, intermediate of hydrogen ··Y)setare in Figure 3.bonding In this paper, the distance parameter R was set to that of a ··· chemical bond non-bond. Hydrogen is Ralso special bond Y) in and Figure 3. In this paper, the distance wasaset toforce, 3 Å, chemical and the 3between Å, andbond the (X–H angle β are wasshown set to 120°.a Hydrogen bonding is bonding aparameter weak interaction intermediate ◦ . Hydrogen bonding is a weak interaction force, intermediate between that of angle β was set to 120 [35–39] formed atoms that have large electronegativities (suchisas O, aF special and S) combined with between that of between a chemical bond and a non-bond. Hydrogen bonding also chemical bond a chemical bond and a non-bond. Hydrogen bonding is also a special chemical bond [35–39] formed a hydrogen atom and aatoms covalent to adjacent atoms with (such large as electronegativity. Hydrogen [35–39] formed between thatbond have large electronegativities O, F and S) combined with between atoms that have large electronegativities (such as O, F and S) combined with a hydrogen atom comprise both and intramolecular interactions abonds hydrogen atom andintera covalent bond to adjacent atoms [33]. with large electronegativity. Hydrogen
R β
X(
X D o (D o no no r) r)
bonds
and a covalent bond to adjacent atoms with large electronegativity. Hydrogen bonds comprise both comprise inter- and intramolecular interactions [33]. inter- andboth intramolecular interactions [33]. ) tor p e c Ac r) Y( pto e c (Ac R Y
β Hydrogen
Hydrogen
Figure 3. The definition of hydrogen bond. X represents the donor, which can form a chemical bond 3. atom; The definition of hydrogen bond. X represents donor, which can can bond form with a hydrogen Yofrepresents the acceptor, which can form a which hydrogen a hydrogen Figure 3.Figure The definition hydrogen bond. X represents thethe donor, formawith achemical chemical bond bond with a hydrogen atom; Y represents the acceptor, which can form a hydrogen bond with atom.a hydrogen atom; Y represents the acceptor, which can form a hydrogen bond with a hydrogen with atom.
a hydrogen atom.
3.1. Effect3.1. of Effect Temperature of Temperature 3.1. Effect of Temperature The number of hydrogen bonds and the mechanical parameters of the P_W0 and P_W4 models The number of hydrogen bonds and the mechanical parameters of the P_W0 and P_W4 models at
temperatures indicated in 4 and 5, respectively. at different temperatures areareindicated inFigures Figures 4 and 5, parameters respectively.of the P_W0 and P_W4 models Thedifferent number of hydrogen bonds and the mechanical
at different temperatures are indicated in Figures 4 and 5, respectively.
Number of hydrogen bonds Number of hydrogen bonds
80
80 70 70 60 60 50 50 40 40 30 30 20
(P-W0)-Htotal (P-W00)-H )-Htotal intra (P-W (P-W00)-H )-Hintra inter (P-W
(P-W4)-Htotal (P-W44)-H )-Htotal intra (P-W (P-W44)-H )-Hintra inter (P-W
20 10
(P-W0)-Hinter
(P-W4)-Hinter
10 0
383 403 423 Temperature (K) 383 363 403 343 423 Temperature (K) forfor Figure 4.Figure Number of hydrogen bonds at atdifferent temperatures meta-aramid fiber molecules. 4. Number of hydrogen bonds different temperatures meta-aramid fiber molecules. 0
343
363
Figure 4. Number of hydrogen bonds at different temperatures for meta-aramid fiber molecules.
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KP-W0
EP-W0
GP-W0
(C12-C44)P-W0
KP-W4
EP-W4
GP-W4
(C12-C44)P-W4
0.6 0.4
12
0.2
10
0.0
K、 E、 G (GPa)
14
8
-0.2
6 -0.4
4
C12-C44 (GPa)
18
-0.6
2
-0.8
0 343
383 403 363 Temperature (K)
423
Figure 5. 5. Mechanical Mechanical parameters parameters of of meta-aramid meta-aramid fibers fibers at at different different temperatures. Figure temperatures.
Figure 4 shows that, with the temperature temperature rise, rise, there there was was no no regularity regularity in in the the number number of of interinterand intramolecular hydrogen bonds of the meta-aramid fibers. The temperature variation fluctuated slightly in each paired set of data. When When the the moisture moisture content was 4%, the number number of hydrogen hydrogen bonds between the themolecular molecular chains of meta-aramid fibers was significantly lower than in the chains of meta-aramid fibers was significantly lower than that in thethat anhydrous anhydrous state; the difference between the average numbers hydrogen bonds in two state; the difference between the average numbers of hydrogen bondsof in the two conditions wasthe 24.87%. conditionsin was 24.87%. Therefore, in a transformer environment, impact of temperature on the Therefore, a transformer environment, the impact of temperature the on the hydrogen-bond network of hydrogen-bond network of meta-aramid fibers is not obvious, and moisture is an important factor meta-aramid fibers is not obvious, and moisture an important factor damaging the hydrogen-bond damaging network of the fibers. network ofthe thehydrogen-bond fibers. The overall variations of Figure 5 showed that, with the increase of temperature, the parameters K, E and G decrease slightly, slightly, whereas whereasCC12 12–C44 showed rising trend, trend, though though the the change change was was relatively relatively 44 showed aa rising slow. slow. In the temperature environment of a transformer, the mechanical properties of the meta-aramid fibers decrease slightly with a temperature rise. This This is is due due to the arrangement of the molecular structure of of the the meta-aramid meta-aramid fibers and and the the existence existence of a large large number number of of hydrogen hydrogen bonds bonds between between the molecular chains. consistent with the conclusions conclusions in in the the literature literature [40]. [40]. Compared Compared the molecular chains. This This result result is is consistent with the with the the P_W P_W00 model, the P_W P_W44 model with model, the the tensile, tensile, volume, volume, and and shear shear moduli moduli of of the model were were small small and and the the Cauchy was high. high. These mechanical properties the meta-aramid meta-aramid Cauchy pressure pressure was These results results show show that that the the mechanical properties of of the fibers combined analysis of the datadata in Figure 4 shows that fibers were were lowered loweredby bythe thepresence presenceofofwater. water.A A combined analysis of the in Figure 4 shows the main reason for this observation is that the intermolecular hydrogen-bond network of the metathat the main reason for this observation is that the intermolecular hydrogen-bond network of the aramid fibersfibers was was destroyed, and and the the interactions between thethe fiber meta-aramid destroyed, interactions between fiberchains chainswere werereduced reduced by by the the presence of moisture. presence of moisture. The showed that,that, in theinoperating environment of a transformer, a rise in temperature The above abovedata data showed the operating environment of a transformer, a rise in will lead to will a decrease the mechanical properties of the meta-aramid fibers;fibers; specifically, the temperature lead to aofdecrease of the mechanical properties of the meta-aramid specifically, intermolecular hydrogen-bond network of the meta-aramid fibers is destroyed due to the presence the intermolecular hydrogen-bond network of the meta-aramid fibers is destroyed due to the presence of which affects affects these these properties. properties. of moisture, moisture, which As one of the main aging products oil–paper insulation system, moisture is an As one of the main aging productsofofa atransformer transformer oil–paper insulation system, moisture is important factor affecting the mechanical properties of the aramid fibers. Considering the common an important factor affecting the mechanical properties of the aramid fibers. Considering the common hot-spot for further further dynamic dynamic hot-spot temperature temperature of of power power transformers, transformers, the the temperature temperature was was set set at at 403 403 K K for simulations. The mechanism of the effect of moisture on the mechanical properties and thermal simulations. The mechanism of the effect of moisture on the mechanical properties and thermal stability of the the meta-aramid meta-aramid fibers fibers was was further further explored explored in in this this condition. condition. stability of 3.2. Analysis of Hydrogen Bonds of of thethe hydrogen bonds of the fibersfibers with Figure 66 shows showsthe thestatistical statisticalcharacteristics characteristics hydrogen bonds of meta-aramid the meta-aramid different moisture contents. with different moisture contents.
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0
Number of water molecules 16 24 33 42
Htotal P-Hinter P-Hintra (P-W)-H
200
Number of hydrogen bonds
8
78 3.0
Haverage
2.5
160
2.0
120
1.5 1.0
80
Haverage
240
0.5 40 0.0 0 0%
1%
2% 3% 4% 5% Percentage of water mass
9%
Figure 6. Hydrogen Hydrogen bond characteristics of composite models with different moisture contents.
It can can be be seen seen that that water water molecules molecules and and meta-aramid meta-aramid fibers form a a large large number number of of hydrogen hydrogen It fibers form bonds; the the number number of of hydrogen hydrogen bonds bonds ((P–W)–H) ((P–W)–H) formed formed with with water water molecules molecules and and meta-aramid meta-aramid bonds; fibers showed a rising trend with increasing water content. The number of intermolecular fibers showed a rising trend with increasing water content. The number of intermolecular hydrogen hydrogen bonds (P–H (P–Hinter inter))in bonds inthe themeta-aramid meta-aramidfibers fibers was was reduced, reduced, and and the the number number of of intramolecular intramolecular hydrogen hydrogen bonds (P–H (P–Hintra intra) )of P_W00 model, moisture bonds of the the fibers fibers remained remained unaffected. unaffected. Compared Compared with with the the P_W model, the the moisture contents of the composite models were 1%, 2%, 3%, 4%, 5% and 9%, and their respective percentage contents of the composite models were 1%, 2%, 3%, 4%, 5% and 9%, and their respective percentage decreases in innumbers numbersofof intermolecular hydrogen bonds 10.34%, 21.14%, decreases intermolecular hydrogen bonds werewere 10.34%, 21.14%, 25.86%,25.86%, 34.45%,34.45%, 32.76% 32.76% and 36.21%. In general, the of number of hydrogen bondsmeta-aramid between meta-aramid fiber chains and 36.21%. In general, the number hydrogen bonds between fiber chains decreased decreased with the increase in moisture content. with the increase in moisture content. There is is an an important important relationship relationship [33] [33] between between the the hydrogen hydrogen bonds bonds formed formed between between the the high high There molecular mass polymer and their mechanical properties. It can be seen that the positions of the fibers molecular mass polymer and their mechanical properties. It can be seen that the positions of the that are first affected by moisture are those betweenbetween the molecular chains. With theWith increase fibers that are first affected by moisture arelocated those located the molecular chains. the of moisture content,content, the hydrogen bond bond network of meta-aramid fiber was increase of moisture the hydrogen network of meta-aramid fiber wasdestroyed, destroyed,and and its its mechanical properties reduced. Similar conclusions can be found in the literature [30]. Through the mechanical properties reduced. Similar conclusions can be found in the literature [30]. Through the analysis of average) formed between the water molecules and analysis of the theaverage averagenumber numberofofhydrogen hydrogenbonds bonds(H(H average ) formed between the water molecules meta-aramid fibers, a downward trend was observed after the upward was at a and meta-aramid fibers, a downward trend was observed after the upwardtrend. trend.The TheHHaverage average was at maximum when the moisture content was 3%, indicating that the hydrogen bonding between a maximum when the moisture content was 3%, indicating that the hydrogen bonding between water water molecules and molecules and meta-aramid meta-aramid fibers fibers reached reached saturation. saturation. When When the the moisture moisture content content was was less less than than 3%, 3%, the binding effect of the meta-aramid fibers on moisture increased with increasing moisture content; the binding effect of the meta-aramid fibers on moisture increased with increasing moisture content; when hydrogen hydrogen bonding bonding between between moisture moisture and and meta-aramid meta-aramid fibers fibers reached reached saturation, saturation, the the binding binding when effect of ofthe thefibers fibers water molecules started to decrease. This can explain why, the effect onon thethe water molecules started to decrease. This can explain why, when thewhen moisture moisture content exceeds 3%, the fiber structures are damaged by moisture, the damage is more content exceeds 3%, the fiber structures are damaged by moisture, the damage is more severe with severe withmoisture increasing moisture and thestability combined stability of the meta-aramid increasing content, andcontent, the combined of the meta-aramid fiber chainsfiber andchains water and water molecules will gradually decrease. molecules will gradually decrease. 3.3. Free Volume In accordance with the free volume theorem, the volume of high molecular mass polymers comprises two parts: the the occupied volume (VOO)) of of the the macromolecules macromolecules and and the so-called empty macromolecules. Fractional free free volume volume (FFV) (FFV) is the ratio [41] of the free volume not occupied by the macromolecules. volume (VFF)) to volume to the the total total volume volume of of these these polymers. polymers. The The free free volume volume of of aa high high molecular molecular mass mass polymer polymer important effect effect on onthe thediffusion diffusionofofsmall smallmolecules. molecules.InInthis thiswork, work,the theVan Van der Waals radius has an important der Waals radius of of2H O in meta-aramid fiber system calculated using hard-ball probe model the H O2in thethe meta-aramid fiber system waswas calculated using the the hard-ball probe model [42],[42], and and the free free volume of the water molecules was calculated from the Van der Waals radius. The calculated results are shown in Table 1.
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Polymersof 2017, 537 8 of 14 volume the9,water molecules was calculated from the Van der Waals radius. The calculated results are shown in Table 1. Figure7 7shows showsa aschematic schematicdiagram diagramofofthe thefree freevolume volumeofofmeta-aramid meta-aramidfibers fiberswith withdifferent different Figure moisture contents. moisture contents.
Figure 7. 7.Free (a) P_W P_W00; ;(b) (b)P_W P_W ; Figure Freevolumes volumesofofcomposite compositemodels modelswith with different different moisture moisture contents. contents. (a) 1;1(c) (c)P_W P_W ; (d) P_W ; (e) P_W ; (f) P_W ; (g) P_W . 2 3 4 5 9 2; (d) P_W3; (e) P_W4; (f) P_W5; (g) P_W9.
From 1, 1, the FFV Fromthe thedata dataininTable Table the FFVvalues valuesofofmeta-aramid meta-aramidfibers fiberswith withdifferent differentmoisture moisturecontents contents were 1% <
