Molecular size distribution in synthesis of polyoxymethylene dimethyl ethers and process optimization using response surface methodology

Accepted Manuscript Molecular Size Distribution in Synthesis of Polyoxymethylene Dimethyl Ethers and Process Optimization using Response Surface Methodology Yanyan Zheng, Qiang Tang, Tiefeng Wang, Jinfu Wang PII: DOI: Reference:

S1385-8947(14)01388-6 http://dx.doi.org/10.1016/j.cej.2014.10.056 CEJ 12799

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Chemical Engineering Journal

Please cite this article as: Y. Zheng, Q. Tang, T. Wang, J. Wang, Molecular Size Distribution in Synthesis of Polyoxymethylene Dimethyl Ethers and Process Optimization using Response Surface Methodology, Chemical Engineering Journal (2014), doi: http://dx.doi.org/10.1016/j.cej.2014.10.056

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Molecular Size Distribution in Synthesis of Polyoxymethylene Dimethyl Ethers and Process Optimization using Response Surface Methodology Yanyan Zheng, Qiang Tang, Tiefeng Wang*, Jinfu Wang∗ Beijing Key Laboratory of Green Reaction Engineering and Technology Department of Chemical Engineering, Tsinghua University, Beijing 100084, China

Abstract: Polyoxymethylene dimethyl ethers (PODEn, CH3O(CH2O)nCH3, where n ≥ 1) are ideal diesel fuel additives. Among the PODEn compounds, PODE3-5 have the best properties as diesel additives. A theoretical analysis of the molecular size distribution of PODEn synthesized from dimethoxymethane (DMM) and paraformaldehyde (PF) was performed based on a sequential reaction mechanism. The molecular size distribution model follows the Schulz-Flory distribution, and showed a good prediction ability at different reaction temperatures (T) and DMM/CH2O mole ratios (M), which verified the sequential reaction mechanism during the formation of PODEn. The product distribution was optimized using the molecular size distribution model and response surface methodology (RSM). At optimum operating conditions of T = 105 oC and M = 1.1, the conversion of formaldehyde XCH2O has a high value of 92.4%, and the fraction of PODE3-5 in the PODEn mixture is 33.2 wt%, while the fractions of PODEn>5 and PODE2 are 9.4 wt% and 24.3 wt%, respectively. Keywords: Polyoxymethylene dimethyl ethers; Sequential reaction mechanism; Schulz-Flory distribution; Response surface methodology.

∗

Corresponding authors. Tel.: +86 10 62794132; Fax: +86 10 62772051. Email address: [email protected] (T. Wang), [email protected] (J. Wang). 1

1. Introduction Polyoxymethylene dimethyl ethers (PODEn, CH3O(CH2O)nCH3, where n ≥ 1) are receiving much attention as ideal diesel fuel additives, which could significantly reduce the smoke and engine exhaust emissions during combustion [1,2]. The production of PODEn from C1 chemicals, like methanol and formaldehyde, can fully utilize the large surplus of C1 chemicals [3], alleviate the diesel supply crisis, and thus bring enormous economic and environmental benefits. The studies on the synthesis of PODEn are very limited in the literature, and most of them are experimental studies on the synthesis reaction [4-8]. Zhao et al. [4] studied the synthesis of PODEn from methanol and trioxymethylene using molecular sieves as catalysts. In this system, water is produced during the formation of methylal. Because water reacts with formaldehyde and PODEn, the side reactions are notable in this reaction system and make the product purification process very complex [5]. To avoid this problem, Burger et al. [5,6] investigated the synthesis of PODEn from dimethoxymethane (DMM, namely PODE1) and trioxymethylene, and obtained 23.6 wt% yield of PODE3-4. However, trioxymethylene is more expensive as a source of formaldehyde and more prone to form PODEn>5 compounds, compared with paraformaldehyde (PF) [8]. In our previous work, we reported the synthesis of PODEn from dimethoxymethane (DMM) and PF over cation exchange resins [8]. Under optimized conditions, the conversion of formaldehyde was 85.1%, and the fraction of PODE3-5 in the product was 36.6 wt%. In the PODEn compounds, only the PODE3-5 compounds are ideal diesel additives, because PODE2 does not fulfill the security criterion due to its low flash point, and PODEn>5 precipitate at low temperatures due to their high melting points [2,6]. Therefore, the PODE2 and PODE n>5 compounds need to be separated and 2

recycled to the reactor in an industrial process [6]. The overmuch production of PODE2 or PODE n>5 would significantly increase the energy cost. When recycled into the reactor, a portion of PODEn>5 reacts with formaldehyde and forms larger PODEn compounds, leading to a complicated separation and recycling process. Therefore, it is of great importance to study the molecular size distribution of PODEn and optimize the process conditions to improve the molecular size distribution. The molecular size distribution is most studied in polymer chemistry. Knowledge of molecular size distribution is significant not only for inferring the properties of polymers [9], but also for a better understanding of the reaction mechanism [10]. The Schulz-Flory (SF) distribution [11-13] and Poisson distribution [14-16] are the most widely used theoretical molecular size distributions. Generally, the SF distribution is based on the precondition of constant probability of chain growth [17]. In addition to its wide applications in conventional processes like polycondensation and free radical addition polymerization processes, the SF distribution is also used in Fischer-Tropsch synthesis [18-20] and carbon nano-tube (CNT) preparation [21]. The other theoretical molecular size distribution, namely Poisson distribution, is considered to be a fundamental distribution for the conventional living polymerization [10,22]. The living polymerization refers to a polymerization of organic molecules when termination is avoided but the true equilibrium is not reached [23]. Zhao et al. [24] found that the product distribution follows the SF distribution during the synthesis of PODEn, but did not derive the molecular size distribution model based on reaction mechanism. The response surface methodology (RSM) is a collection of statistical and mathematic techniques, and has been widely used to develop, improve and optimize a process [25-30]. The use of RSM highly enhances the experiment and optimization

3

efficiency. Based on the designed experimental data, the RSM gave a functional relationship between the response and the independent variables. In this work, a theoretical analysis of the molecular size distribution of PODEn synthesized from DMM and PF was performed based on a sequential reaction mechanism. During the process optimization in synthesis of PODEn, both the molecualr size distribution and conversion of formaldehyde should be considered. The optimization of the molecualr size distribution and conversion of formaldehyde was carried out using RSM. To the best of our knowledge, this is the first report on theoretical analysis of the molecular size distribution of PODEn and optimization of the molecular size distribution by RSM.

2. Materials and methods 2.1. Materials DMM (analytic reagent grade, AR) was purchased from Alfa Aesar-Johnson Matthey. PF (analytic reagent grade, AR) was purchased from Sinopharm Chemical Reagent Co., Ltd. The NKC-9 cation exchange resins were dry resins of H+ type provided by Tianjin Bohong Resin Technology Co., Ltd. 2.2. Synthesis of PODEn The reaction experiments were carried out in a 0.5-L stirred autoclave operated in batch. For each experiment, the mixture of PF and DMM was first loaded in the reactor. To obtain the equilibrium concentration data, the reaction proceeded until the concentrations became unchanged with time on stream. The composition of the PODEn mixture was quantitatively analyzed by gas chromatography-mass spectrometry (GC-MS). The product sample (0.5 mL) was diluted with 5 mL of undecane. 1.0 L of the solution was injected into a Shimadzu 2010 plus GC equipped with an MXT-5 column (5% diphenyl/95% dimethyl 4

polysiloxane, 30 m × 0.25 mm× 0.1 µm) and a flame ionization detector (FID). The column temperature program comprised two stages: the initial temperature was set at 40 °C for 5 min, which was then ramped to 320 °C at 20 °C/min and held for 10 min. Nitrogen was used as carrier gas. An Agilent G2579A MS was used to identify the species with different residence times in the GC column. Because no gas or solid byproducts were formed, the carbon balance was good, with error within ±5%. The overall selectivity to PODEn>1 was over 98% at the experimental conditions in this work. In the following theoretical analysis, the equilibrium conversion of formaldehyde (XCH2O) refers to the mass fraction of formaldehyde converted when the system reached equilibrium, and was calculated by:

X CH2O =

NCH2O, feed − N CH2O, product

(1)

N CH2O, feed

Where the amount of formaldehyde (mol) in the feedstock ( N CH 2O, feed ) and in the equilibrium system ( N CH 2O, product ) were determined by the method provide by ASTM D2194-02 (2012). To evaluate the product distribution, a product distribution index (PDI) is defined as follows:

PDI = w3-5 − θ1wn >5 − θ 2 w2

(2)

where θ1 and θ2 are the relative coefficients of PODEn>5 and PODE2, respectively. A larger PDI means a compromise result of a higher yield of target product PODE3-5 and lower yields of the by-products PODEn>5 and PODE2. Considering that PODEn>5 is more undesirable than PODE2 as discussed in section 1, θ1 is set to be larger than θ2. The values θ1 and θ2 can be adjusted according to the process demand. Herein, θ1 and θ2 were set as 0.9 and 0.3, respectively. 5

2.3. Process optimization using RSM To optimize the process of PODEn synthesis, both the molecular size distribution (reflected by PDI) and the conversion XCH2O should be considered. In this reaction system, PDI and XCH2O are determined by the reaction temperature (T) and DMM/CH2O molar ratio (M). While the effect of the reaction time on PDI and XCH2O will be investigated in future work on kinetics. In the present work, RSM with 5-level and 2-factor central composite design (CCD) was used to optimize the PDI and XCH2O. For two independent variables, the axial parameter is 1.414 for rotatable CCD. The experiment was designed for 5 levels of varying independent variables which were coded as -1.414, -1, 0, +1, and +1.414, as shown in Table 1. Considering the temperature tolerance of NKC-9 resin, the center value and step size of T are set as 75 oC and 15 oC, respectively. The center value and step size of the variable M are 2 and 1, respectively. Multiple regression analysis was used to derive the second-order polynomial equations to predict the PDI and XCH2O. A general second-order polynomial equations [26] can be expressed as:

PDI = β0, P + β1, P x1 + β2, P x2 + β11, P x12 + β22, P x22 + β12, P x1 x2

(3)

X CH 2 O = β0,X + β1, X x1 + β2, X x2 + β11, X x12 + β22, X x22 + β12, X x1 x2

(4)

where x1 and x2 are the coded independent variables, namely the temperature (T) and DMM/CH2O molar ratio (M), respectively; β0 , P and β0 , X are the intercept coefficients;

β1,P , β2,P , β1, X and β2, X are the linear coefficients; β11,P , β22, P , β11, X and β22, X are the quadratic coefficients; and β12,P and β12,X are the interaction coefficients.

3. Molecular Size Distribution Model 3.1. Mechanism for PODEn formation from PF and DMM In our previous work, a sequential reaction mechanism was proposed for the 6

synthesis of PODEn from DMM and PF, as shown in Fig. 1 [8]. According to this mechanism, the PF molecule depolymerized to formaldehyde monomers, and PODEn-1 and formaldehyde react to form PODEn. This coincides well with the experimental phenomena that PODE2 was firstly formed, and then PODE3, PODE4 ··· PODE7 appeared one by one during the synthesis of PODEn. This also excludes another mechanism proposed in literature [6] that the PF molecular breaks into segments (CH2O)n, and (CH2O)n reacts with DMM to form PODEn+1 in one step, which would lead to a simultaneously formation of PODEn components with different polymerization degree. In addition, it was found that when the reactants were PODE2 and PF, both PODEn>2 and DMM were produced. This indicated that the polymerization reactions to PODEn were reversible. Therefore, the propagation of the polymerization involves the following reactions: k

p DMM + CH2 O ← → PODE2 k

(5)

d

k

p PODE i + CH 2O ← → PODEi +1 kd

(i = 2, 3 … n)

(6)

where kp and kd are the rate constants of the forward (polymerization) and reverse (depolymerization) reactions, respectively. Since the PODEn compounds are homologous series, kp and kd are assumed to be independent of n. 3.2. Equilibrium Molecular Size Distribution Model

When the reaction system reached equilibrium, the amounts of all the species are constant [31], i.e. ∞

∞

n =1

n= 2

dN CH2O, e / dt = −kp N CH2O, e ∑ N n ,e + kd ∑ N n,e = 0

(7)

dN1,e / dt = −kp N CH 2O, e N1,e + kd N 2,e = 0

(8)

dN n,e / dt = kp N CH 2O, e ( N n−1,e − N n ,e ) + kd ( N n+1,e − N n,e ) = 0

(n=2, 3…)

where N CH2O, e , N1,e and Nn,e are the equilibrium moles of formaldehyde, DMM and 7

(9)

PODEn in the liquid phase. Based on the reaction mechanism, the total amount of PODEn (n ≥ 1) is equal to the initial amount of DMM, therefore ∞

∑ N n,e = N1，0

(10)

n =1 ∞

∑ N n ,e = N1，0 − N1,e

(11)

n=2

where N1,0 is the initial amount of DMM. Substitution of Eqs. (10) and (11) into Eq. (7) gives (12)

N CH2O,e = kd (1 − N1,e / N1,0 ) / kp

Combination of Eqs. (10), (11) and (14) yields

N n,e = N1,e (1 − N1,e / N1，0 )n −1

(13)

The total amount of the added CH2O groups equals to the amount of reacted formaldehyde (denoted by N CH2O, R , exclusive of the formaldehyde converted to by-products as discussed in section 2.2). This gives: ∞

N1,0

n =1

M

∑ (n − 1) N n,e = N CH2O,0 X CH 2O =

(14)

X CH2O

where N CH2O,0 is the initial amount of formaldehyde, X CH2O is the equilibrium conversion of formaldehyde and M is the initial DMM/CH2O molar ratio. For convenience, a dimensionless factor ae is defined as the ratio of N CH2O, R to N1,0 at equilibrium:

ae = N CH2O, R / N1，0 =

X CH 2O

(15)

M

Thus Eq. (14) can be expressed as ∞

∑ (n − 1) N n ,e = N1，0 ae

(16)

n =1

8

Combining Eq. (13) and (16) gives

N1,e =

N n,e N1，0

N1，0

(17)

1 + ae

 a  a  = 1 − e  e   1 + ae  1 + ae 

n −1

(18)

This is the equilibrium molecular size distribution of the PODEn products. It follows the SF distribution, where ae/(1+ae) corresponds to the probability of chain growth. The weight fraction distribution could be calculated by  M DMM + M CH 2O (n − 1)  ae n−1 wn =   M DMM + M CH O ae  (1 + ae )n  2 

(19)

where wn is the mass fraction of PODEn compound. In this system, the depolymerization of PF is the rate-determining step, while the reversible chain growth reactions are in a pseudo-equilibrium state at any transient moment. Therefore, the molecular sized distribution is also applicable for transient product distribution data, which would be further discussed in future work on kinetics.

4. Results and Discussion 4.1. Prediction ability of the theoretical molecular size distribution model

The natural logarithm form of Eq. (19) is ln

  wn a 1 = n ln e + ln   n + 1.533 ae + 1  ae (2.533 + ae ) 

(20)

Eq. (20) shows that the equilibrium mass fractions of the PODEn compounds are determined by the factor ae and degree of polymerization n. For a specific ae, the molecular size distribution of the PODEn compounds can be calculated by Eq. (20). Typical results of the molecular size distribution with different values of ae are shown in Fig. 2. When the value of ae varied in the range of 0−2.5, the mass fraction curves

9

of PODE2 and PODE3-5 show single-peak patterns. The mass fractions of PODE2 and PODE3-5 reach their maximum value of 25 wt% and 38 wt% at ae of 0.7 and 1.7, respectively. In contrast, the mass fraction of DMM monotonically decreased and that of PODEn>5 monotonically increased with increasing ae. The parameter PDI was used to evaluate the product distribution at different ae. The variation of PDI with ae is also shown in Fig. 2. The PDI curve has its peak value of 17.5 when ae is 1.1. Therefore, it is desirable to optimize the operating conditions to make the PDI value close to 17.5, which corresponds to a high yield of PODE3-5 and reasonable by-production of PODEn>5 and PODE2. Experiments at different T and M were carried out to check the model prediction ability, and the results are shown in Figs. 3 and 4. The plots of ln(wn/(n+1.533)) with respect to n showed a good linear relationship, with R2 > 0.99. This confirms that the theoretical model has a good prediction ability for the molecular size distribution. The calculated value of ae,cal was determined from the slope (or intercept) of the line between ln(wn/(n+1.533)) and n. The calculated values of ae,cal from the slope and from the intercept are consistent within the deviation allowed (± 3 %), as shown in the inserted tables in Figs. 3 and 4. The measured mass fractions of the PODEn compounds are very close to the calculated values. The experimental value ae,exp was determined by XCH2O/M according to its definition. The experimental and calculated values of ae agreed very well, as shown in Fig. 5. These results further validate the sequential reaction mechanism [8] and the molecular size distribution mode proposed in this work. 4.2. Experimental results and statistical analysis using RSM

For process optimization using RSM, the parameters PDI and XCH2O are the important factors. The experimental design matrix and the experimental results are

10

shown in Table 2. The analysis of the experimental results in Table 2 was performed using the software Design-Expert V8.0.6.1, and the manual regression model was selected to fit Eqs. (3) and (4). The resulted coefficients of Eqs. (3) and (4) are listed in Table 3. For the two models, the predicted R2 is in a reasonable agreement with the adjusted R2, indicating that the models well described the relationship between the independent variables and the response. The p-value was an important factor to evaluate the statistical significance of each regression term. The p-values less than 0.05 indicate that the regression terms are significant [26-27]. All the regression terms are significant, among which x2 (coded DMM/CH2O molar ratio) is the most significant term due to its least p-value. This indicates that the DMM/CH2O molar ratio has the most significant effect on XCH2O. The statistical significance of the models was tested by the analysis of variance (ANOVA), as shown in Table 4. The sum of squares is an index used to estimate the square of deviation. The mean squares are estimated by dividing the sum of squares by degrees of freedom. The model F-value was used to evaluate the overall significance of the model, in which the calculated value of F should be greater than the F-table value [26-27]. Herein, the model F-values of 1038.36 and 39.40 imply that the two models were statistically significant. The operating region, where T varies from 45 oC to 105 oC and M varies from 0.5 to 4.0, is the feasible optimization range considering the tolerable temperature of the catalyst and system pressure. Fig. 6 shows the contour plots of PDI as a function of T and M. It can be seen that the increase of T and decrease of M would increase PDI. In order to obtain a high yield of PODE3-5 and avoid overmuch by-production of PODEn>5 and PODE2, the optimum of PDI is around 17.5, as discussed in 3.2. When the operating parameters is on the line segment between (T = 78 oC, M = 0.5) and (T =

11

105 oC, M = 1.1), the PDI reaches the value of 17.5, thus obtaining 33.2 wt% of PODE3-5 compounds in PODEn, while controlling the mass fraction of PODEn>5 and PODE2 at 9.4 wt% and 24.3 wt%, respectively. The conversion of formaldehyde XCH2O is another essential index. Fig. 7 shows the contour plots of XCH2O as a function of T and M. In general, operation at high T or high M is favorable to increase XCH2O. The synthesis of PODEn from DMM and PF is endothermic and reversible, therefore the conversion of formaldehyde increases with an increase in the reaction temperature and DMM/PF ratio. In the two subtriangular regions, (T = 45oC, M = 2.2)-(T = 55 oC, M = 4.0)-(T = 65 oC, M = 2.8) and (T = 105 o

C, M = 0.5)-(T = 78 oC, M = 2.75)-(T = 105 oC, M = 3.4), the XCH2O is over 80%. But

in the former region, the reactions are too slow due to the low operating temperature, and the higher M means a lower conversion of DMM. Therefore, only the latter subtriangular region is feasible and optimal. To optimize the synthesis of PODEn, both PDI and XCH2O should be considered. In the contour of PDI = 17.5, the point (T = 105 oC, M = 1.1) is optimum, giving the highest XCH2O of 92.4%.

4. Conclusions Among the PODEn compounds, PODE3-5 compounds are the most ideal diesel additives. A theoretical molecular size distribution model of PODEn from DMM and PF was proposed based on the sequential reaction mechanism. The product distribution was optimized using the molecular size distribution model and response surface methodology (RSM). The following conclusions can be drawn from the theoretical analysis and experimental results: (1) The molecular size distribution model followed the SF distribution.

12

(2) The molecualr size distribution model showed a good prediction ability at different T and M, which verified the sequential reaction mechanism of PODEn synthesis from DMM and PF. (3) The molecular size distribution and formaldehyde conversion were optimized using RSM, and the optimum operating conditions were determined as T = 105 o

C and M = 1.1, where the formaldehyde conversion reached 92.4%, and the

fraction of PODE3-5 in the PODEn mixture was 33.2 wt%, while the fractions of PODEn>5 and PODE2 were 9.4 and 24.3 wt%, respectively.

NOMENCLATURE N CH2 O, e = equilibrium amount of formaldehyde (mol)

kp = reaction rate constants of the forward reactions (s-1) kd = reaction rate constants of the reverse reactions (s-1) N1,e = equilibrium amount of DMM (mol) Nn,e = equilibrium amount of PODEn (mol) N1,0 = initial amount of DMM (mol) N CH2 O, R = the amount of reacted formaldehyde

M = DMM/CH2O molar ratio X CH2 O = equilibrium conversion of formaldehyde

ae = dimensionless factor n = polymerization degree of PODEn wn = mass fraction of PODEn

13

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Figures caption: Fig.1. Sequential reaction mechanism for the formation of PODEn from PF and DMM Fig.2. Relationship between the molecular size distribution and PDI in PODEn with the factor ae. Fig.3. Applicability of the theoretical molecular size distribution model at different DMM/CH2O molar ratios (M). Fig.4. Applicability of the theoretical molecular size distribution model at different reaction temperatures (T). Fig.5. Comparison between calculated value ae,cal from Eq.(18) and experimental value ae,exp from Eq.(13). Fig.6. Contour plots of factor PDI (production distribution index) as a function of reaction temperature (T) and DMM/CH2O molar ratio (M). Fig.7. Contour plots of XCH2O as a function of reaction temperature (T) and DMM/CH2O molar ratio (M).

18

Table 1. Coding of independent variables T and M Coded level Independent variables

-1.414

-1

0

+1

+1.414

T: reaction temperature

53.79

60

75

90

96.21

M: DMM/CH2 O molar ratio

0.59

1

2

3

3.41

19

Table 2. Experimental design matrix and results Independent variables

Coded variables

T (oC)

M (mol/mol)

x1

x2

1

75

2

0

2

75

2

3

60

4

Test No.

PDI (-)

XCH2O (%)

0

4.76

76.2

0

0

4.80

76.2

3

-1

1

1.33

81.0

53.79

2

-1.414

0

4.33

72.0

5

75

2

0

0

4.76

76.2

6

90

1

1

-1

4.76

75.2

7

60

1

-1

-1

10.65

56.6

8

75

2

0

0

4.80

76.0

9

90

3

1

1

1.10

79.2

10

75

2

0

0

4.72

76.4

11

96.21

2

1.414

0

7.05

90.2

12

75

3.41

0

1.414

-0.14

77.5

13

75

0.59

0

-1.414

15.59

45.5

20

Table 3. Coefficient values of response surface model (the correct use of significant figure) Model for PDI (Eq.(19))

Model for XCH2O (Eq.(20))

Value

p-value

Value

p-value

β0

4.75

<0.0001

76.2

<0.0001

β1

1.01

<0.0001

5.3

0.0009

β2

-5.70

<0.0001

9.2

<0.0001

β11

0.55

0.0005

2.9

0.0265

β22

1.57

<0.0001

-6.3

0.0003

β12

-1.17

<0.0001

-5.1

0.0070

R2

0.9987

0.9657

Adjusted R2

0.9977

0.9412

Predicted R2

0.9905

0.7563

Adeq precision

100.131

21.830

Coefficient

21

Table 4. Analysis of variance (ANOVA) for the response surface models Source

Sum of squares

Degree of freedom

Mean square

F-value

1038.36

Model for PDI (Eq.(19)) Regression

291.14

5

58.23

Residual

0.39

7

0.0056

Lack-of-fit

0.39

3

0.13

Pure error

3.121E-003

4

7.803E-004

Total

291.53

12

Model for XCH2O (Eq.(20)) Regression

1442.24

5

288.45

Residual

51.25

7

7.32

Lack-of-fit

51.17

3

17.06

Pure error

0.080

4

0.020

Total

1493.49

12

22

39.40

Fig. 1. Sequential reaction mechanism for the formation of PODEn from PF and DMM

23

Fig. 2. Relationship between the molecular size distribution and PDI in PODEn with the factor ae.

24

Fig. 3. Applicability of the theoretical molecular size distribution model at different DMM/CH2O molar ratios (M).

25

Fig. 4. Applicability of the theoretical molecular size distribution model at different reaction temperatures (T).

26

Fig. 5. Comparison between calculated value ae,cal from Eq. (18) and experimental value ae,exp from Eq.(13).

27

Fig. 6. Contour plots of factor PDI (production distribution index) as a function of reaction temperature (T) and DMM/CH2O molar ratio (M).

28

Fig. 7. Contour plots of XCH2O as a function of reaction temperature (T) and DMM/CH2O molar ratio (M).

29

Highlights





Theoretical analysis of PODEn molecular size distribution (MSD) was performed The MSD model was based on a sequential reaction mechanism. The MSD model follows the Schulz-Flory distribution. Response surface methodology was used to optimize the MSD.

30