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The effect of the pH value of the anodic solution on the transmembrane transport of oxygen in the cathode chamber in microbial fuel cells
AbstractIn this paper, a molecular dynamic model

is established to describe the transfer of oxygen in the cathode chamber through the Nafion membrane to the anode chamber of MFCs.The effect of the pH values of the anodic solution on the diffusion process is studied and the diffusion coefficient are calculated either. The law of oxygen transmembrane transport predicted by simulations is validated by experiments. The results of molecular dynamic simulationsshow that the diffusion coefficient of oxygen molecules increases sharply with the decrease of the pH value of the MFCs anodic solution. It appears that the lower the pH value is, the more easily the oxygendiffusesinto the anode chamber.This conclusion is coherent with experimental results.The diffusion coefficient of hydronium ions is almost unchanged after the rise at first with the decrease of the pH value and has the saturation because of the limitation of the Nafion membrane ion exchange capacity. The radial distribution functionanalysis shows that the main factors affecting the oxygen molecules transmembrane diffusion are the free volume and motion of Nafion side chains. Keywords Microbial Fuel Cells, pH value, dissolved oxygen, diffusion coefficient, free volume 1. Introduction Microbial fuel cells (MFCs) can convert the chemical energy of organic compounds into electric energy directly through the action of microorganism and have the dual effects of productivity and environmental restoration[1-4].A typical MFC is composed of the anode chamber, cathode chamber, and a separator.Proton exchange membrane (PEM) is the most common MFC separator [5]. The MFCs using PEMas separator have two main problems: the accumulation of protons in the anode chamber and the leakage of oxygen in the cathode chamber [6]. In the initial stage of battery operation, the concentration of the chemical cations(such as Na+、 K+、 Ca2+、 Mg2+ and NH4+) 5 is usually 10 times as much asprotonsin the anodic solution, these cations bind to the acidic group of PEM preferentially and inhibit the transmembranetransport of protons, resulting the accumulation of protons andthe decreaseof the pH value of the anode solution [7-10].Protons depletedby cathode cannot be added in time, so that the pH value of the cathodic solution increases, the cathode potential dropsand the system output voltage decreases. Meanwhile, the decrease of the pH value of the anodic solution also inhibits the growth of themicroorganism [11].PEM is a kind of high molecular polymerand its porous structure makes the transmembrane transport of oxygen in the cathode chamber hard to avoid.If there is oxygen in the anode chamber, for the concurrent anaerobic bacteria, oxygen will replace the anode electrode as electron acceptor during the metabolic process; for anaerobic bacteria, oxygen will seriously inhibit its growth [12], and the Coulombicefficiency of MFCs will reducesignificantly.Studying the relationship between the two main problems above can provide a new approach to solve them. At present, researches on the internal mass transfer process in MFCs using PEM as separators are mainly through experiments. Chae et al. [6] measured the change of the dissolved oxygen, pH value, cations and acetate concentration with time in the anode and cathode chambers respectively and obtained the effect on the output voltagein the course of runningin MFCs using Nafion117 as separators. Pant et al. [13] compared the diffusion behavior of oxygen in air cathode MFCs using

different membranes. He found that the diffusion coefficientof oxygen transfer through Zirfon is less than that through Nafion and it can be used as a substitute of the expensive Nafion and Funasep membranesin MFCs.In addition, the influence of membrane biofouling on the mass transfer process and the performance of the battery havealso been studied extensively [14-15].But the research on the relationship betweenthe pH value of the anodic solution and the diffusion of oxygen in the cathode chamber is rarely reported and it’s difficult for experiments to explain the microscopic mechanism of a process. Because Nafion(DuPont,USA)which is the most widely usedcommercialPEM of MFCs, hasthe highest penetration of oxygen [16],in this paper, we established a molecular dynamic model to describe the transmenbrane transport of oxygenin the cathode chamber in MFCs. Wechose 5 groups of the pH values of the anodic solution which decreased with time in the initial stage of battery operation as the independent variables,calculated the diffusion coefficients of oxygen molecules and other structures in Nafion under different pH conditions respectively.The effect of the pH values of the anodic solution on the transmenbrane transport of oxygen in the cathode chamber was also investigated.To verify the law of diffusionderiving fromsimulation results and experiments, qualitative analysis was carried outaccording to the radial distribution function (RDF) and the free volume theory. 2. Model establishment 2.1 Model parameters Because the scale of molecular dynamics simulations is much smaller than the physical size of MFCs and the duration ofthe diffusion process, in order to reflect the transmenbrane transport of oxygen, the model is established according to the physical and chemical conditionsderiving from the surface of Nafion membrane contacting the anodic solution of MFCs. Materials Studio (MS) 8.0 is used to buildthe cell models to simulate the oxygen molecules diffusion in Nafion. A cell model contains hydration Nafion molecules, water molecules, hydronium ions and oxygen molecules (When Nafion molecules meet water, the O-H bondsof the sulfonic acid group of the side chain will break to form hydration Nafion molecules andhydronium ions). Figure 1 shows the structural formula and MS drawing result of the hydration Nafion molecule, of which m is 7, n is 10 , andthe degree of polymerizationis10[17].

(a)Hydration Nafion molecule [18](b)MS drawing result Figure 1. The structure of the hydration Nafion

After drawing the basic structure, the number of each structure needs to be confirmed. The number of hydration Nafion molecular chains is confirmed at first.The Gierke cluster-network model [19-21] which is recognized and obtained by the small angle X ray diffraction experimentis used as modeling basis. Figure 2 shows the C-C main chains of hydration Nafion aggregating and formingspherical structures which are connected by some short narrow passages. The sulfonic

acid groupsof the side chains are surrounded into the spherical structures to act as the ion transport medium. When the Nafion membrane is swollen with water, the diameter of each spherical ion cluster is 4-5nm and narrow passage is 1nm. There are also approximately 70 sulfonic acid groups and 1000 water molecules in each swollen spherical structure.The average diameter of the ring structure in Figure 1b is 4.3nm, just in line with the spherical ion clusters, and the degree of polymerization of it is 10, so the number of sulfonic acid groups is 10. According to those above, we confirm that the number of hydration Nafion molecular chains is 7 and signify that there is only one spherical ion clusterin a cell model.

Figure 2.Diagram ofGierke cluster-network model [19-21],the blue part is C-C main chain, the gray part is side chain and the red dot is sulfonic acid group

The number of water moleculesand the density of the cell model are confirmed secondly. The micro membrane moisture contentλshows the ratio of the number of water molecules (Including water molecules in hydronium ions) to sulfonic acid groups.The value of λis from 11 to 13 approximately whenNafion membrane is fully wet. To match with the Gierke cluster-network model,λis assumed as 13, which means the total number of water molecules and hydronium ions is 910. According to the formula in reference [22], the density of thecell model is 1.764g· cm-3 as λis 13. 2.2 The number of oxygen molecules Calculating the diffusion coefficient of oxygen molecules in Nafion membrane under neutral condition and then comparing the results with the experimental data from reference [6] to confirm the number of oxygen molecules.Reference [6] suggests that the diffusion coefficient of oxygen molecules which were calculated based on the dissolved oxygen (DO) was 5.27× 10-6cm2· s-1 as the anodic solution was distilled water, and it was 5.35× 10-6cm2· s-1 as the anodic solution was the phosphate buffer respectively when DO in the cathode chamber was saturation and in the anode chamber was 0.85mg· L-1 in an uninoculated MFC. Under neutral condition, hydronium ions in the cell model are all derived from the hydrolysis ofsulfonic acid groupsof side chains of Nafion molecules. On the basis of section 2.1, the number of hydronium ionsin the cell model is confirmed as 70, which is equal to the number of sulfonic acid groups. The number of water molecules is 840. 6 groups of cell models were established according to the different number of oxygen molecules (15, 16, 17, 18, 19, 20). The algorithm of geometry optimization is Smart and the quality is Fine. The energy minimization process is Anneal in MS Forcite and the quality is Fine either. Annealing cycles are 5, the initial temperature is 298K and the Mid-cycle temperature is 698K. Every 40K is a temperature interval of heating or cooling and dynamics steps per ramp is 100 choosing NVT ensemble and Andersen thermostat. The time step is 1 fs and total number of steps is 10000. Only after optimization of the cell model can we calculate thediffusion coefficient of oxygen molecules. The formula of the self-diffusion coefficient in MS is [17]:

D=

1 d N 2 lim ? ([r i (t ) ? r i(0)] ) (1) 6 N t ?? dt i ?1
2

N is the number of diffusion particles, MSD=?[r i(t ) ? r i(0)] ? , is the mean square displacement, (MSD) 。 MS output trajectory document can recordthe MSD with time and makean average of the number of particles, so the self-diffusion coefficient D can be directlycalculated based on the slope of therelation curve between MSD and time Obtaining the trajectory documentmentioned above by Forcite module, the ensemble is NVE and the temperature is 298K. The time step is 1 fs and total simulation time is 50ps. The total number of steps is 50000 and frames output every 50 steps, providing 1000 frames to calculate and analyze.The simulation results of those 6 cell models above are listed in Table 1.
Table 1 The diffusion coefficients of oxygen molecules and hydronium ions in the 6 cell models The number of oxygen molecules The diffusion coefficients of oxygen molecules× 10 cm · s The diffusion coefficients of hydronium ions× 10 cm · s
6 2 6 2 -1

15 9.03 4.17

16 8.35 3.72

17 7.46 3.24

18 6.58 2.53

19 5.67 2.05

20 4.25 1.52

-1

Table 1 data shows that when the number of oxygen molecules in the cell model is 19, the calculation result of oxygen diffusion coefficient is closestto the experimental data in reference [6]. So in the subsequent calculation of the diffusion coefficients of oxygen molecules under different pH conditions, the number of oxygen molecules is selected as 19. Table 1 data also shows that if the number of oxygen molecules in the membrane increases gradually with time, the oxygen mass transfer gradient andthe diffusion coefficient will be reduced with it. 2.3 The diffusion coefficients of oxygen molecules under different pH conditions The simulation mainly considers the diffusion phenomenon rather thanelectromigration under the effect of electric field, so the pH value of the anodic solution is confirmed according to the experimental date when the outer resistance of MFCsis infinite in reference [23]. We assume that the cell model is taken from the surface of Nafion membrane contacting the anode solution.The date in reference [23] shows thatthe pH value of the anode solution decreased from 7 to 6.60 nearlyin 500hand gradually stabilized at around 6.80 in the end, thus the interval of the pH value is 7.00 to 6.80. The concentration of hydronium ions in the cell model is proportional to its number. Section 2.2 has suggested that the number ofhydronium ions is 70 under neutral condition, using aH to show the concentration of hydronium ions in the cell model and assuming a constant cwhich means other conditions are unchanged in addition to the number of hydronium ions,thus there is the following formula:

pH ? -lg aH ? -lg(70c) ? 7 (2)
If the pH value is 6.80, thenumber of hydronium ionsin the cell model isassumed asx, then:

pH ? -lg aH ? -lg( xc) ? 6.8 (3)
Formula (2) divided by (3 ):
70c 10?7 (4) ? xc 10?6.8 x is approximately equal to 111 by solving formula (4), which realizes the multi scale

coupling of the macroscopic solution pH value and the micro number of hydronium ions. Reserving the integer part ofxandmaking 10 as interval to establish5 groups of the cell modelwhich are marked as A, B, C, D, E. The number ofhydronium ions in each model is 70, 80, 90, 100, 110 and the corresponding pH value is 7.00, 6.94, 6.89, 6.85,6.80respectively.There are 7 Nafion molecule chains and 19 oxygen molecules in each cell model. Establishment and optimization of models and calculation of the diffusion coefficients are according to the methods in section 2.2. 3. Experimental validation The interval of the pH value of 5 groups of the cell model in the simulation is 0.05. In order to highlight the difference of the pH value and reduce the influence of other unknown factors on the accuracy of experimental results, the interval of the pH value in experiments is increased to 0.5. In this chapter, 3 groups of the acetic acid solution with different pH values (5.5, 6.0, 6.5) were prepared. The change of the DO and oxygen transmembrane diffusion coefficient with time was measured during the process of oxygen in the air transferring through Nafion117 into the solution with different pH values, which can be usedto qualitatively verifythe simulation resultsmentioned above. 3.1 Materials 250mL RO water was injected into a PET bottle with volume of 480mLand the DOprobe(CellOx 325, WTW, Germany) was inserted into the bottle. The device wasaeratedwith nitrogen untilthe DOofthe RO water was less than 1.9 mg· L-1.The mouth of the bottle was sealed by a rubber plug and hot melt adhesive. The PET bottle and the DO meter (Oxi 3310, WTW, Germany) were put into a 25℃ light incubator (GXZ intelligent, Ningbo Jiangnan Instrument Factory, China) with air circulating in it. The change of the temperature and the DO of the RO water in the PET bottle with time was recorded every 10min and the total time was 3h. Figure 3 shows the result of the air tightness test of the PET bottle used above. The DO in Figure 3was measured under the temperature 24.8±0.1℃ of the RO water. Figure 3suggests that the DO of the RO water in the PET bottlefluctuates in the vicinity of 1.93mg· L-1, which means that the PET bottle has a good barrier effect on the oxygen in the air.

2.4

2.2

DO/(mg· L )

-1

2.0

1.8

1.6

1.4

Figure 3The DO of the RO water in the PET bottle Time/min

0 10 20 30 40 50 60 70 80 90 100 110 120 130

Arectangularwindow (size: 1.5cm× 3cm)was opened in the side of the PET bottle. Took out Nafion117 membrane (size: 2.5cm× 4cm, DuPont, USA) which had been soaked over 24h in the deionized water.The membrane was tightly covered and fixed on the rectangular window and the gap was sealed withtape and hot melt adhesive.Then injected the RO water into the bottle and

ensured that the rectangular window wassubmergedin the water totally.If there was no water oozing from the gap after 24h, then the sealing performance was proved to meet the experimental requirements. 3.2 The effect of the different pH values on the oxygen transmembrane transport Prepared the solution, of which pH value was 5.5and volume was 300mL, by RO water and acetic acid. Measured off 250mL and injected into the PET bottle made in section 3.1. The rectangular window was submergedin the solution totally. The DO probewas inserted into the bottle and the device wasaeratedwith nitrogen until the DOwas less than 0.5 mg· L-1. The mouth of the bottle was sealed by a rubber plug and hot melt adhesive. The PET bottle and the DO meter were put into a 25℃ light incubatorwithair circulating in it, as is shown in Figure 4. The change of the temperature and the DO of the solution in the PET bottle with time was recorded every 10min and the total time was 20h.Poured the solution and rinsed the bottle inside after recording the data. Prepared the solution of which pH value was 6.0 and repeated those experimental steps above, obtained the change of the DO with time. In the same way, the change of the DO with time as the pH value of the solution was 6.5 could also be obtained.

Figure 4Schematic diagram of the experimental device, the peripheral frame is the light incubator

In section 3.1, the air tightness of the PET bottle used in the experiment had been verified and the rectangular window was submerged in the solution during the experiments. So we assumed that the oxygen in the air was diffused totally through Nafion membrane into the solution after opening the window and covering with Nafion in the side of the bottle.Thus, the mass transfer coefficient of oxygen in the air transporting through Nafion117 into the solution in the PET bottle can be calculated using the following formula [6]:
Ko ? ? v ? C0 ? C ? ln ? ? (5) At ? C0 ?

v is the liquid volume in the PET bottle, Ais the area of the rectangular window, C0is the content of oxygen in the air (Because the volume fraction ofoxygen in the air is 21%, C0=300mg· L-1), Cis the DO of the solution in the bottle at time t. The diffusion coefficient of oxygen is calculated usingDo=KoL, where L=183μmis the membrane thickness 4. Results and discussions 4.1 Results of simulations Not only the diffusion coefficients of oxygen molecules had been calculated, the diffusion coefficients of other structures, such as hydronium ions, water molecules, the typical atom C of

Nafion main chains and the typical atom O and S of Nafion side chains had also been calculated.The position of atom C, S and O of Nafion molecules is shown in Figure 5. The 6 kinds of structures above aredistinguishedaccording to the type of the force field. The simulation results of the diffusion coefficients are shown inTable 2 and Figure 6.

Figure 5 Nafion molecule Table 2The diffusion coefficients of oxygen molecules and other structures
Diffusioncoefficient× 106cm2· s-1

Oxygen molecule 5.67 12.80 18.47 21.33 27.83

Water molecule 3.87 15.67 23.67 22.95 21.67

Hydronium ion 2.05 4.43 10.57 10.74 10.90

C of main chains 1.64 3.03 4.87 5.14 5.93

S of side chains 2.07 4.37 5.33 6.17 7.33

O of side chains 1.53 2.93 4.76 4.93 5.40

Group /pH A/7.00 B/6.94 C/6.89 D/6.85 E/6.80

30

8

Diffusion Coefficient×10 cm · s

Diffusion Coefficient×10 cm · s

2

2

25 20 15 10 5 0 65

Oxygen molecule Water molecule Hydronium ion

7 6 5 4 3 2 1 65

C of main chains S of side chains O of side chains

-1

6

70

75

80

85

90

95 100 105 110 115

6

-1

70

75

80

85

90

95 100 105 110 115

The number of hydronium ions

The number of hydronium ions

Figure 6The diffusion coefficients of oxygen molecules and other structures

The data in Table 2 and Figure 6 shows that the diffusion coefficient of oxygen molecules increases sharply with the decrease of the pH value of the anodic solution of MFCs.When the pH is 7.00, the diffusion coefficient of oxygen molecules is 5.67× 10-6cm2· s-1, but it increases rapidly to 27.83× 10-6cm2· s-1which is about 5 times as much as it under neutral conditiononly when the pH decreases 0.20 to 6.80.It appears that in the early stage of MFCs operation, the transmembrane transport of cathodic oxygen is very sensitive to the pH value of the anodic solution.The proton accumulation in the anode chamber not only makes no contribution to suppress the diffusion of oxygen in the cathode chamber but also makes the process more likely to occur. Although in the actual operationprocess ofMFCs, the oxygen molecules transmembrane transport is mainly

affected by theDO gradient in the solution of the two sides of the membrane, the gradient decreases with the increase of running time, and the diffusion coefficient of oxygen molecules decreases with the change of the gradient, however, in the early stage of MFCs operation, the anodic solution DO is lower and the protonsaccumulate rapidly, the main trend will bethe increase of the diffusion coefficient of oxygen molecules caused by the decrease of the pH value.Therefore,the growth limitation of the anodic microorganism and the change of the electron acceptor caused by oxygen leakage in the cathode chamber are the main reasons for the increase of the battery startup time and the decrease of the MFCs efficiency. The diffusion coefficient ofhydronium ions is almost unchanged after the rise at first with the decrease of the pH value of MFCs anodic solution.When the pH value is reduced to 6.89 and decreasescontinually, the diffusion coefficient only increasesslightlyon the basis of 10.57× 10-6cm2· s-1. In the 5 cell model groups, the diffusion coefficient ofhydronium ions is obviously smaller than that of oxygen molecules and water molecules,it is showed that the characteristic of positive charge has a significant effect on the diffusion ofhydronium ions. In group A and B, the number of hydronium ions is 70 and 80 respectively, which is considerableto 70 sulfonic acid groups in the cell model. And the diffusion coefficient of hydronium ions is close to that of S atom of side chains. It suggests that the hydronium ion is mainly affected by the Coulomb force and adsorbed on the sulfonic acid groupof the side chain of Nafion molecules anddiffused by it.In group C, D and E, the number of hydronium ions is 90, 100 and 110 respectively,which is significantly more than the number of sulfonic groups, and the diffusion coefficients of hydronium ions in these 3 groups are proximal,which means the transmembrane transportation of hydronium ions has the saturation because of the limitation of the Nafion membrane ion exchange capacity.It seems that the sole increase of the mass transfer gradient cannot promote the diffusion of hydronium ions to the cathode chamber to participate in the reduction reaction.To optimize the battery performance, it is necessary to adjust the MFCsmembrane materials and solution conditions. In the 5 groups of cell model, the diffusion coefficient of C atom of main chains is considerable to that of O atom of side chains, less than S atom of side chains and other free molecules or ions. Combined with Figure 5, the law mentioned above is corresponding to the position of different atoms in Nafion, which suggests that themotionof side chainsis fiercer than C-C main chains 4.2 Results of experiments According to the interval and the total length of the experimentaldata recordtime in section 3.2, we know that each group will get 121 data points.Chose the data points of which the solution temperature in the bottle was stabilized at 24.7 ± 0.1 ℃ to analyze. Fordifferent pH valueconditions, DO= 0.82mg· L-1was selected as the starting point and 34data points wereselectedcontinuouslyin each group for analysis. Then the change of the DO of the solution in the bottle with time and the diffusion coefficient of oxygen in the air through the Nafion117 membrane into the solution at each moment are shown in Table 3 and Figure 7.
Table 3 The DO of the solution in rhe PET bottle and the transmembrane diffusion coefficients of oxygen pH=5.5 Time(min)
DO mg· L
-1

pH=6.0
DO
2 -1

pH=6.5
DO
2 -1

Diffusion coefficient× 10 cm · s
7

Diffusion
-1

Diffusion
-1

mg· L

coefficient× 10 cm · s

7

mg· L

coefficient× 107cm2· s-1

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330

0.82 0.89 0.91 0.93 0.95 0.98 1.05 1.08 1.11 1.16 1.19 1.21 1.23 1.28 1.32 1.35 1.33 1.32 1.33 1.35 1.39 1.41 1.44 1.49 1.5 1.52 1.69 1.57 1.55 1.64 1.73 1.66 1.64 1.85

/ 50.34 25.74 17.54 13.44 11.09 9.90 8.73 7.85 7.29 6.73 6.23 5.80 5.57 5.34 5.09 4.71 4.40 4.18 4.02 3.93 3.80 3.71 3.67 3.54 3.44 3.68 3.29 3.13 3.20 3.27 3.03 2.90 3.18

0.82 0.84 0.86 0.87 0.87 0.87 0.87 0.89 0.95 0.95 0.97 0.99 1.00 1.02 1.02 1.01 1.02 1.04 1.07 1.09 1.11 1.13 1.14 1.15 1.15 1.13 1.22 1.2 1.18 1.22 1.24 1.26 1.27 1.27

/ 47.51 24.32 16.40 12.30 9.84 8.20 7.19 6.72 5.97 5.49 5.09 4.71 4.44 4.12 3.81 3.61 3.46 3.36 3.25 3.14 3.04 2.93 2.83 2.71 2.56 2.66 2.52 2.38 2.38 2.34 2.30 2.25 2.18

0.83 0.85 0.84 0.91 0.89 0.89 0.89 0.93 0.94 0.91 0.92 0.93 0.93 0.94 0.96 0.99 0.98 0.99 0.99 1.00 1.02 1.05 1.07 1.15 1.13 1.11 1.15 1.13 1.19 1.19 1.2 1.21 1.21 1.19

/ 48.08 23.76 17.16 12.59 10.07 8.39 7.52 6.65 5.72 5.20 4.78 4.38 4.09 3.88 3.73 3.47 3.29 3.11 2.98 2.89 2.83 2.75 2.83 2.66 2.51 2.50 2.37 2.41 2.32 2.26 2.21 2.14 2.04

50

Diffusion coefficient×10 cm · s

1.8

1.6

7

pH=5.5 pH=6.0 pH=6.5

-1

45 40 35 30 25 20

pH=5.5
6

pH=6.0

pH=6.5

2

5

DO/(mg· L )

-1

4

1.4

3

2

1.2

15 10 5 0 0 50

100

150

200

250

300

1.0

0.8

0

Time/min (a)The DO of the solution Time /min in the PET bottle(b)The diffusion coefficients of oxygen

50

100

150

200

250

300

100

150

200

250

300

Figure 7The results of experiments

The data in Table 3 and Figure 7 shows thatunder the condition of 3 groups of different pH values of the solution, the DO of the solution in the PET bottle both increasesignificantly with time. When the pH value is 5.5,6.0 and 6.5, the increment of the DO is 1.03, 0.45 and 0.36mg· L-1 respectively. It suggests that the lower the pH value of the solution, the more easily the oxygen diffuses into the solution.This conclusion is corresponding to the simulation result above. The increments of the DO of 3groups cannot compose an arithmetic sequence, the increment in pH=5.5 is obviously greater than the other 2 groups, which means the effect of the pH value on the transmembrane diffusion of oxygen is nonlinear, the smaller the pH value of the solution is, the more significant the effect is. The increase of the DO of the solution in the PET bottle willlead to the decrease of the oxygen concentration gradient between the two sides of the Nafion117 membrane. The transmembrane diffusion coefficient of oxygen is related to this gradient and time of the mass transfer, therefore, it decreases rapidlyat first and decline slowly after that.Figure 7b shows that when the pH value of the solution is smaller, the oxygen diffusion coefficient is greater, which is corresponding tothe change of the DO, and the effect of the pH value is also nonlinear. In section 2.2, the number of oxygen molecules in the cell model was confirmed according to the diffusion coefficient of oxygen molecules when the DO of the anodic solution was 0.85 mg· L-1in reference [6]. And thenumber of oxygen molecules is 19 in the following calculation consistently. Thus, the DO of the anodic solution of the simulation results in Table 2 can be assumed to 0.85mg· L-1. The experimental data of the diffusion coefficient at 10min is selected to compare with the results of simulations.The simulationresultsshow that when the pH is 7.00, the diffusion coefficient of oxygen molecules is 5.67× 10-6cm2· s-1 and it increases rapidly to -6 2 -1 27.83× 10 cm · s when the pH decrease by 0.20 to 6.80.The results of experimentsshow that when the pH decreases from 6.5 to 5.5, the transmembrane diffusion coefficient of oxygen increases from 4.81× 10-6cm2· s-1 to 5.03× 10-6cm2· s-1. Although there is an increment,it is significantly smaller compared with the simulation value.Two reasons lead to the difference. On the one hand, the diffusion coefficient is closely related to the time interval and the time start, it is not an absolute value. On the other hand, the physical and chemical conditions are different, the simulation assumes that both sides of the Nafion117 membrane are solution, and in the experiments, two sides of the membrane are solution and air respectively.

4.3 Radial distribution function analysis The reason of the difference of the diffusion coefficients of oxygen moleculesin Nafion with the change of the pH values of the anodic solution is analyzed from the microscopic point of view. According to the free volume theory [24-26], the main factors affecting the diffusion rate of gas molecules in the membraneare temperature, the size of the gas molecules and the free volume fraction of the polymer membrane.In the simulations of this paper, the temperature is 298K, the gas molecules are only oxygen, so the analysis mainly uses the free volume fraction.And on this basis, we combine with the distribution of free volume and the situation of polymer chain motionto make the specific analysis. The free volume of the cell model is mainly distributed between water, Nafion main chain and side chain molecules according to the model composition and the number of each structure.Due to the number of water molecules is far more than the other structures, the free volume of water molecules is dominating.The free volume fraction of 5 groups of the cell model is shown in Table 4.It can be seen that the free volume fraction increases at first and decreasesthenand reaches the maximum value in group C.
Table 4 The free volume fraction of the cell model Group/pH A/7.00 B/6.94 C/6.89 D/6.85 E/6.80 Occupied volume/A3 72481.47 73285.20 73413.62 72603.17 73297.04 Free volume/A3 15386.08 15580.64 16781.24 15914.56 15500.10 Total volume/A3 87867.55 88865.84 90194.86 88517.73 88797.14 Free volume fraction/% 17.51 17.53 18.61 17.98 17.46

Radial distribution function (RDF) is defined as the probability of finding the atom B at a distance ofrfrom the reference atomA, and the expression is [18]:
nB N ) / ( B ) (6) 4? r 2 dr V In the formula (6), nB is the number of particle B in the shell which thickness is drat the distance ofrfrom the reference particle A. NB and Vare the total number of particle B and the volume of the system respectively.g(r) is non-dimensional and can be interpreted as the ratio of regional density and average density.Whenr is larger, RDF is close to 1.The free volume distribution and the polymer chain motion can be obtainedby analyzing the RDF of different atoms. The RDF go-o(r)of water molecules was analyzed at first. RDF was obtained from the MS trajectory document. The Cutoff was 10A and the Interval was 0.02A. The maximum valueof go-o(r) and the corresponding rareshown in Table 5.The RDF curves of water moleculesof the 5 groups of the cell model are shown in Figure 8. gA-B ? r ? ? (
Table 5 The maximum of RDF of water molecules Group/pH r/A A/7.00 2.71 B/6.94 2.71 C/6.89 2.71 D/6.85 2.73 E/6.80 2.71

go-o(r)

6.84

5.08

4.40

4.84

5.60

7

The RDF of water molecules

6 5 4 3 2 1 0 2.0

The number of hydronium ions:

70 100

80 110

90

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

r/A Figure 8The RDF curves of water molecules when r is from 2.0 to 4.0
The data in Table 5 and Figure 8 shows thatwhen the pH value of the anodic solution is gradually reduced, the position of the maximum valueof the RDF curves of water moleculesis almost unchanged. However, the maximum of go-o(r)decreasesfrom6.84 of group A to 4.40 ofgroup Cand rise to 5.60 of group E.It shows that the distance between water molecules is smaller under the neutral condition and then gradually increases.But when the pH value is less than 6.89, the distance between water moleculesgradually decreases.This change law is not only correspondingto the change of free volume fractionwith the pH value of 5 cell models, but also corresponding to the change of the diffusion coefficients of water molecules which increases at first and then decreases with the pH value. Both of the maximum values are in group C.It suggests that the free volume of water molecules is the main component of the free volume of the cell, the change law of it is the change law of the free volume of the cell, the greater the water molecular spacing is, the larger the free volume of the cell is, the greater the water molecular diffusion coefficient is. The RDFgc-c(r)of C atom of Nafion main chains was analyzed secondly.The Cutoff was 10A and the Interval was 0.02A. In the 5 groups of the cell model, each gc-c(r)curvehas 3 maximum values in the cutoff distance. The maximum values of gc-c(r) and the corresponding r are listed in Table 6.
Table 6 The RDF maximum values of C atom of Nafion main chains Group/pH A/7.00 B/6.94 C/6.89 D/6.85 E/6.80

r1/A
1.51 1.51 1.51 1.51 1.51

gc-c(r1)
35.52 34.60 37.11 38.62 35.17

error/%
-1.89 -4.43 2.50 6.67 -2.86

r2/A
2.49 2.47 2.49 2.47 2.47

gc-c(r2)
28.03 25.87 25.74 28.49 24.89

error/%
5.36 -2.76 -3.25 7.09 -6.44

r3/A
3.75 3.73 3.73 3.73 3.73

gc-c(r3)
4.92 4.97 4.76 4.98 5.41

error/%
-1.76 -0.76 -4.95 -0.56 8.03

gc-c(r) average

36.20

26.60

5.01

The data in Table 6 shows that the positions of the maximum value of RDF curves of C atom of Nafion main chainsin 5 groups of the cell model are the same.The values of gc-c(r1), gc-c(r2) and gc-c(r3) are less different and there is no obvious regularity change with the decrease of the pH value.It suggests that the change of the pH value has nearly no effect on thespacing of C atomsof main chainsof Nafion. The free volume of Nafion main chain is the fixed component in the free volume of the cell. It is not related to the change of the cell free volumeand is not the main factor affecting the diffusion of oxygen molecules in the membrane. The RDF gc-s(r)between O atom of Nafion main chains and S atom of Nafion side chains was analyzed at last. The two large extreme values of RDF curves and the change of the corresponding position were mainly researched.The Cutoff was 10A and the Interval was 0.02A. The maximum values of gc-s(r) and the corresponding r are listed in Table 7
Table 7 The RDF maximum values between O of main chains and S of side chains Group/pH A/7.00 B/6.94 C/6.89 D/6.85 E/6.80

r1/A
2.69 2.69 2.69 2.69 2.69

gc-s(r1)
25.90 22.01 21.33 21.05 20.84

r2/A
4.29 4.31 4.35 4.35 4.37

gc-s(r2)
2.11 2.78 2.62 2.67 2.56

Distance between r1 and r2/A 1.60 1.62 1.66 1.66 1.68

The data in Table 7 shows that when the pH value decreases gradually, gc-s(r1) decreases from 25.90 of group A to 20.84 of group E, and r1 are both 2.69A. It suggests that the density of S atoms in the vicinity of the main chain C atoms decreases and the number of S atoms reducegradually. The deviation between r1 and r2 increases from1.60 to 1.68 which means the distance between C and S atoms also increases gradually. According to the change law of the diffusion coefficient of oxygen molecules in Table 2, we indicate that the free volume of Nafion side chains is the main factor affecting the diffusion of oxygen molecules in the membrane.The decrease of the pH value is equal to the increase of the number of hydronium ions in the cell model.Due to the positive charge of hydronium ions, the increase of the number of hydronium ions is bound to change the distribution of the Coulomb force in the cell modeland affect the motion of the Nafion side chains which have sulfonic acid groups of the unit negative charge, thus, changes the relative position of main and side chains of Nafion molecules and affects the diffusion of oxygen molecules in the membrane. Figure 1 shows that the C-C main chain of Nafion molecule is covered by F atoms. This structure is stable and hydrophobic.In the cell model, the main chains form a hydrophobic tubular structure, in which the diffusion resistance of oxygen molecules is much less than that in the spacing of water molecules.When gc-s(r1) is greater, the distance between C and S atoms is smaller, the side chain is mainly into a bendas it shown in Figure 6.When gc-s(r1) decreases gradually with the decrease of the pH value, the distance between C and S atoms increases. It suggests that the motion of side chains is getting intense on the one hand and the bending degree of side chains is reduced and is similar to the hydrophobic tubular

structure of the C-C main chainwhich is beneficial to the diffusion of oxygen molecules on the other hand. Therefore, the diffusion coefficient of oxygen molecules in Nafion increases with the decrease of the pH value ofthe anodic solution of MFCs. 5. Conclusions In this paper, in order to studythe effect of the pH value of the anodic solution on the transmembrane transport of oxygen in the cathode chamber in MFCs, according to the physical and chemical conditions deriving from the surface of Nafion membrane contacting the anodic solution of MFCs, a molecular dynamic model was established to describe the transfer of oxygen in the cathode chamber through the Nafion membrane to the anode chamber.Chose 5 groups of the pH value of the anodic solution which were decreased with time in the initial stage of battery operation as independent variables to reflect theproton accumulation,calculated the diffusion coefficients of oxygen molecules and other structures under different pH conditions respectively and qualitative verified the law of oxygen diffusion deriving from simulations by experiments and analyzed it according to RDF and the free volume theory at last.The main conclusions are as follows: (1)The simulation results show that the diffusion coefficient of oxygen molecules increases sharply with the decrease of the pH value of MFCs anodic solution. When the pH value is 7.00, the diffusion coefficient of oxygen molecules is 5.67× 10-6cm2· s-1. When the pH value is reduced to 6.80, it rises to 27.83× 10-6cm2· s-1 rapidly and approximately 5 times higher than it under neutral condition. It appears that the lower the pH value of the anode solution is, the more easily the oxygen in the cathode chamber diffuses to the anode chamber. This conclusion is coherent with experimental results. Meanwhile, it appears that in the early stage of MFC operation,the growth limitation of the anodic microorganism and the change of the electron acceptor caused by oxygen leakage in the cathode chamber are the main reasons for the increase of the battery startup time. (2)The transmembrane transportation of hydronium ions has the saturation because of the limitation of the Nafion membrane ion exchange capacity. The diffusion coefficient of hydronium ions is almost unchanged after the rise at first with the decrease of the pH value of MFCs anodic solution. It seems that the sole increase of the mass transfer gradient cannot promote the diffusion of hydronium ions to the cathode chamber to participate in the reduction reaction. (3)The free volume of water molecules is the main component of the free volume of the cell, the change law of it is the change law of the free volume of the cell, the greater the water molecular spacing is, the larger the free volume of the cell is, the greater the water molecular diffusion coefficient is. The free volume of Nafion main chains is the fixed component in the free volume of the cell. The main factors affecting the oxygen molecules transmembrane diffusion are the free volume and motion of Nafion side chains, the larger the free volume of Nafion side chain is, the more intense the movement is, and the transmembrane transport of oxygen molecules is more likely to happen.

References
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