Unravelling Electrochemical Lignin Depolymerization - ACS Publications

Subscriber access provided by Kaohsiung Medical University

Article

Unravelling electrochemical lignin depolymerization Bander Bawareth, Davide Di Marino, T. Alexander Nijhuis, and Matthias Wessling ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.8b00335 • Publication Date (Web): 04 May 2018 Downloaded from http://pubs.acs.org on May 4, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Sustainable Chemistry & Engineering

Unravelling electrochemical lignin depolymerization Bander Bawareth,†,‡ Davide Di Marino,¶,‡ T. Alexander Nijhuis,† and Matthias Wessling∗,¶,‡ †SABIC-Glycols, Oxygenates and Functional Chemicals, 11551 Riyadh, Saudi Arabia. ‡AVT.CVT, Forckenbeckstr. 51, 52074 Aachen, Germany. ¶DWI - Leibniz Institute for Interactive Materials, Forckenbeckstr. 50, 52074 Aachen, Germany. E-mail: [email protected] Phone: +49 241 80 95488. Fax: +49 241 80 92252 Abstract Lignin valorisation via electrochemical depolymerization is a promising approach for commercial application due to its moderate reaction conditions. However, there is no available kinetics model for this reaction. Conventional reaction kinetics equations are inadequate when used for lignin degradation because of the limited kinetics information with respect the reaction mechanism. We suggest to use population balance equations to predict the evolution of molecular weight distribution of lignin with time. Solving the low molecular weight (MW) population balance equations is carried out discretely whereas a continuous solution was implemented for the high MW. Additionally, the model accounts for a recombination reaction for the depolymerized species. The model is capable of predicting the molecular weight distribution of lignin as a function of electrochemical processing time. New experimental results are used to extract kinetics constants for different kraft lignin samples.

1

ACS Paragon Plus Environment

ACS Sustainable Chemistry & Engineering 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Keywords polymer degradation, kinetics modelling, population balance equations, fixed pivot solution, random scission, chain-end scission, molecular weight distribution

Introduction In the presence of climate change evidence, renewable energy and resources have become vital elements for a future sustainable chemical industry. For aromatic feedstock, lignin is nature’s most abundant resource, which is traditionally used as an energy source for pulp industry. Due to its aromatic structure, lignin depolymerization is currently an important topic for generating high-value sustainable lignin-based fuels, chemicals and polymers . 1,2 Lignin can be depolymerized, among other processes, via thermal, photochemical and oxidation. These processes are usually carried out at elevated temperature and pressure. 3 In contrast, electrochemical depolymerization of lignin occurs often at mild conditions, although lack of selectivity and low yields still represent crucial bottlenecks. 4 Relevant parameters for the electrochemical depolymerization are the current denisity, the electrolyte and the electrode material. Stiefel et al. and Schmitt et al. studied these parameters with the aim of producing vanillin. 5,6 Parpot et al. and Tolba et al. investigated the influence of several electrode materials. 7,8 More recently, studies were conducted on the utilization of ionic liquids as electrolytes for lignin electrochemical depolymerization, with the advantage of enhanced stabilitiy of the electrochemical windows. 9,10 During the depolymerization process, the constituents of the polymer are degraded in the same reactor unless they are removed at the optimum reaction residence time. 11–13 In order to control the quantity and quality of the decomposed products, the depolymerization reaction kinetics must be comprehended. 14,15 However, because of the complexity that is attributed to these polymers in terms of high molecular weight and different reactive moieties, their reaction kinetics are complicated. Understanding the kinetics of lignin depolymerization is 2


Page 2 of 41

Page 3 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


a key factor to open up this process to commercial applications. 1

Reaction Kinetics NonConventional

Conventional (Chemical Reaction Network)

(MWD or PCLD)

Deterministic Approach (PBE) Continuos (Moment Method)

Discrete

Statistical Approach (Probabilitis)

Discretecontinuous transformation

Direct Approach

Markov chain theory

Recursive method (Binary Tree)

Figure 1: Schematic relationship of the approaches to describe the kinetics of a chemical reaction There are two main modelling techniques for any reaction kinetics: conventional and non-conventional modelling. 16 The conventional modelling uses the chemical reaction network method to determine the reaction rate equations. The chemical reaction network requires formulating a reaction network pathway, determining the reaction rate constant for every reaction and measuring the products and intermediates concentrations. 17 Gasson et al. carried out kinetics modelling for lignin degradation via the Solvolysis approach. In this approach, a model pathway was mapped which consists of 17 reactions. The resulting mechanism from this study was based on both experiments and literature data. 3 On the other hand, the non-conventional model evaluates the time-dependent evolution of a frequency distribution function, such as molecular weight distribution (MWD), polymer chain length distribution or particle size distribution. Accordingly, the overall reaction rate equations of the cleaved polymer can be obtained. During the depolymerization process, the bulk polymer is cleaved into smaller segments and the change in the distribution pattern 3



can be used to fingerprint the bond cleavage types. There are three different scission types. The first type is random chain scission (random degradation), where the scission takes place randomly at any bond in the polymer backbone. The second and third types are midpoint and endpoint (chain-end) scissions, respectively, which are also called specific degradation. 18 The general reaction schemes can be expressed as follows: • Random degradation: K

A(x0 ) −−R→ A(x) + A(x0 − x) • Specific degradation (chain-end Scission): K

A(x0 ) −−CE −→ A(xi ) + A(x0 − xi ) where xi is the molecular weight (MW) of the specific unit A(xi ) that is detached from a polymer A(x0 ) with a MW of x0 . The rate coefficient for degradation of A(x0 ) are KR (x0 ) in the random scission and KCE (x0 ) in the chain-end scission. A(x) is an unspecific polymer that is cleaved from A(x0 ) and has x MW. For high MW polymer, degree of polymerization (DP) is used instead of MW which is the ratio of MW for each molecule to its monomer. 19 The evolution of the MWD with time can be described by two approaches: a statistic approach and a deterministic approach. 16 The statistic approach is based on probabilistic modelling that accounts for the random probability of the polymer to be degraded as a function of time. The statistical analysis of this approach relies on different methodologies observed during the depolymerization process. It can be determined directly by considering the change in the number average molecular weight or the polydispersity of the polymer with time. 20 Another example is the work done by McDemort et al. where a stochastic model was generated based on transition probabilities of possible reaction pathways of lignin degradation. These pathways occurred for every lignin molecule that has a certain polymer length within a transition time. Every reaction pathway for every lignin molecule is called a Markov chain, and Monte Carlo simulation is used to average these Markov chains. 21,22

4


Page 4 of 41

Page 5 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Furthermore, these statistical approaches can be more complicated by introducing structural randomness of a polydisperse polymer such as lignin. Bose et al. have introduced a binary tree model to predict linear polymer degradation as a series of probabilistic events. 23 Fig. 1 summarizes the different modelling approaches used so far for modelling degradation processes of macromolecules. In contrast, the deterministic approach defines the molecular weight distribution (MWD) of the polymer directly as mass or mole population balance equations (PBE). These equations are governed by the change in time of the concentration of a polymer with a certain chain length. 24 The PBEs are integro-differential equations that is solved either as a continuous or as a discrete function. The continuous function can be solved using the moment method; however, it gives only the important properties of the polymer distribution, which are the number (Mn ) and weight (Mw ) average molecular weight. Conversely, the discrete method can give the concentration for every molecular weight. Due to computational expense, it is impractical to use the discrete method for a polymer with a high chain length (L) where L number of PBEs need to be solved. In order to solve this complexity, Kumar et al. proposed a fixed pivot method to solve the PBE for generation or degradation processes. The fixed pivot is a sectional technique that can contain discrete and continuous domains where the PBE can be solved. 25–27 The early work on polymer degradation using PBE was done by Wang, et al. in 1995. The thermal degradation of poly(styrene-allyl alcohol) in solution was examined theoretically and experimentally. Specific and random depolymerization mechanisms were considered in the model. Styrene and styrene allyl alcohol were produced by specific scission while the polymer is depolymerised via random scission. Subsequently, a set of differential equations was generated for the poly(styrene-ally1 alcohol) depolymerization and the two products generation. Based on these differential equations, shape parameters of the peak are determined, which reflect the changes in the MWD during the reaction. 19 The polymer depolymerization and subsequent monomer degradation can be included

5



in the depolymerization kinetics. This can be done by generating two population balances for the polymer depolymerization and the monomer degradation. An example of this is the work done by Renken, et al. in 1999. A kinetics model was developed for the random scission of mannan followed by the degradation of its monomer. The depolymerization was done by thermal hydrolysis with a rate constant of kH while the degradation rate constant is kD . A ratio of kD /kH was generated and ratio of 2 was found to be adequate to the experimental results. Therefore, the optimum residence time can be found via the dynamic model of the degradation process. 19 Furthermore, the model can include polymer structure effects which can give more information about the accessible and inaccessible surfaces of the polymer. Griggs et al. have considered cellulose as a population of varied chain length which was made of soluble and insoluble substrate. 28 The depolymerization was treated as a heterogeneous catalytic reaction. The structure was assumed to be a cylindrical microfibril that undergoes a depolymerization and solubilization of the surface-accessible cellulose. With time, the particle mass and surface area of the cylinder reduces due to the depolymerization, and the degradation rate decreases accordingly. The objective of this paper is to utilize the PBE to study the depolymerization of lignin in an electrochemical reactor. The model uses the fixed pivot technique to solve the PBEs. To the best of our knowledge, this is the first fundamental work to model lignin degradation by PBE. Subsequently, the model is fitted to own experimental results obtained in a new electro-chemical reactor and kinetics rate constants are extracted.

Materials and Methods Electrochemical depolymerization An electrochemical reactor was built based on previous work in our group. Lignin depolymerization can be achieved by using an electrochemical batch reactor equipped with 3D nickel electrodes. The use of 3D electrodes enhances the electrochemical depolymerization 6


Page 6 of 41

Page 7 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2: 3D view of the Swiss Roll electrochemical reactor and flow sheet of the lignin depolymerization experimental setup. of lignin, due to the increase in active surface. 29 Deeper insight about the electrochemical depolymerisation of lignin is provided in previous works. 4,29 A Swiss Roll electrode assembly was hosted in an acrylic glass tube (Evonik Performance Materials GmbH, Germany). The length of the tube was 15 cm, with an inner diameter of 1.2 cm. The complete reactor volume was filled with the electrode assembly. The assembly consists of two rectangular piece of nickel foam (Ni-4753 Recemat, The Netherlands). Each electrode had a geometric surface of 56.2 cm2 and thickness of 1.63 cm. The specific surface was 5400 m2 m−3 . The electrodes were used as received, without any surface treatment. The two electrodes were interposed with a polymer spacer of the same geometric surface as the electrodes (Naltex® Extruded Netting NO1332 80PP NAT, DelStar Technologies Inc, USA). To connect the two nickel foams with an external power supply, two nickel wires (99.5%, Alfa Aesar, Germany) are put in contact with the two electrodes. The electrodes were then rolled up together to obtain the Swiss Roll assembly. The two wires come out from the two extremities. At this point, the assembly was inserted in the acrylic glass tube, 7



by passing the two wires through a T push-in connector (Landefeld Druckluft und Hydraulik GmbH, Germany). The wire exit of the T connector was sealed and the other exit of the T connector was kept open to pump the lignin solution. Reactor and flow sheet are depicted in Figure 2. Kraft lignin (370959, Sigma Aldrich, Germany) was dissolved in 1 M sodium hydroxide water solution (NaOH, 99%, Sigma Aldrich, Germany). A total volume of 100 ml was recirculated through the reactor at 50 ml min−1 . The electrochemical experiments were performed at room temperature for 7 hours using 5 g L−1 as lignin concentration. Samples were taken at 0, 60, 180, 300, 420 min. A constant potential of 3.5 V was used, resulting in a current of 2.5-4 A. The electrochemical reaction caused a slight increase in temperature of the electrolyte (from 22 to 30 ◦ C in 420 min) and a water loss of 4.9% w/w due to water splitting, side reaction of the electrochemical depolymerization. Calculated current densities were in the range of 40 mA m−2 . Increase of the current was due to increased conductivity resulted from water splitting and minor resistance due to lignin depolymerization. Therefore, the power raised up during the electrochemical process. Detailed data regarding temperature, current and power are presented in Table S3. All chemicals were used as received.

Analytics Size exclusion chromatography (SEC) was used to measure the average molecular weight of the different lignin fractions. Average molecular weight and polydispersity (D = Mw /Mn , where Mw is the weight average molecular weight and Mn is the number average molecular weight) were evaluated. Detailed measurement description were discussed in previous works. 4,29

Theoretical Model The model was developed based on the following assumptions: • The depolymerization reactions are first order. 8


Page 8 of 41

Page 9 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3: Representation of the DP of a polymer into discrete and continuous regions where xi = (vi + v(i−1) )/2, adapted from. 30 • The electrochemical reactor is a batch reactor with fixed temperature, pressure and voltage. The changes in the current and the power were not considered in the model. • The reaction rate coefficient is dependent or independent with the MW. • The MWD can simply follow gamma distribution or actual raw data is required. 14,31 • Basic monomer of lignin is syringyl (S, C11 H14 O4 ) with a MW = 210 g mol−1 . 32 • The product of chain-end scission reaction is assumed to be neither cross-linked nor re-polymerized in the reaction mixture. • Random degradation is a reversible reaction where random recombination is expected. 33

Development of Governing Equations In population balance, the time dependent MWD is denoted by n(x, t). For DP range of x to x + dx, the depolymerization rate can be written as follows: • Random depolymerization: dn(x, t) = −KR (x)n(x, t) + 2 dt

Z

∞

KR (x0 )n(x0 , t)Q(x, x0 )dx0

(1)

x

Equation 1 indicates that the population of n(x, t) is reduced by the random depolymeration in a rate of KR (x)n(x, t) and the population of n(x, t) is increased by a factor of 2 due to the binary fragmentation of n(x0 , t). The random recombination, on the other hand, is the reverse of equation 1. 9



Page 10 of 41

• Random recombination: dn(x, t) = +Kr (x)n(x, t) − 2 dt

∞

Z

Kr (x0 )n(x0 , t)Q(x, x0 )dx0

(2)

x

• specific depolymerization: The specific depolymerization reaction rate has to be described by both the degraded polymer: dn(x, t) = −KCE (x)n(x, t) + dt

Z

∞

KCE (x0 )n(x0 , t)Q(x, x0 )dx0

(3)

x

and the product : dni (x, t) = dt

Z

∞

KCE (x0 )n(x0 , t)Q(x, x0 )dx0

(4)

x

Where: Q(x, x0 ) is the stoichiometric Kernel for the fraction of A(x0 ) that cracks to A(x) which is explained in the supporting information along with the derevation of the PBE’s. 25,34–36 ni is the concentration of the specific product i without considering the product degradation. 19,37,38 Kr is the random recombination rate coefficient. The reaction rate coefficient (KR , KR and Kr ) has to be defined for the chain-end and the random scissions and recombination, respectively. 22,39 The reaction rate coefficient can be either independent or can be expressed as a function of polymer concentration, MW, voltage or other parameters. 40 For reversible oligomerization or low conversion depolymerization, K(x) is independent of MW where the average MW changes slightly with time. 31,41 McCoy had assumed that the rate coefficient is dependent with MW as a power law function, K(x) = kλ xλ where x is the DP or MW and λ is an arbitrary parameter expressing the degree

10


Page 11 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of dependency of the rate coefficient on MW. 42,43 Wang et al. used λ = 1 for coal degradation by pyrolysis process. Similarly, the random scission of poly(methyl methacrylate) was assumed to be linearly dependent with MW. 44,45 Oxidative degradation of polystyrene was also assumed to have λ = 1 while the reaction rate coefficient for thermal decomposition of polystyrene is a second order polynomial function of MW. 46,47 Furthermore λ was set to be equal 2 to describe the chemical cracking of olefins and paraffins. 48 Rarely, the breakage rate coefficient has exponential relation on the particle size. 49

Mathematical Model Solution The discrete to continuous solution is a sectional method by which a polymer with L chain length is divided into two regions, namely discrete and continuous regions, as illustrated in Figure 3. The discrete region covers the low MW or DP region of the polymer distribution where a more accurate solution is required. The continuous region accounts for the high MW or DP side of the polymer. This transformation between the discrete and continuous regions called fixed pivot (FP) technique. In the FP, the grid of the MWD is discretized into L pivots and every pivot represents a DP. The DP data points fall in the continuous region are referred as xi = (vi + v(i−1) )/2 where v is the pivot DP. The DP of the monomer (xm ) has a value of 1. 25–27 The discretizing of the pivots results either a uniform grid or a geometric grid. In the uniform grid, the pivots are positioned within xm units, which represent the discrete region. The geometric grid is used in the continuous region where the pivots are spaced broader than xm . This space is based on the geometric ratio which depends on the DP of the polymer and the location of the boundary (b) between the discrete and the continuous regions. 30 The geometric mesh employed in all the pivots after b which are z + 1 pivots. 25–27 The Geometric 1 ) xb+L ( b−1 xi+1 and r = . ratio is defined by Kostoglou, et al. to be: r = xi xb+1

11



0.03 [a]

= 0.00 = 0.14

-1

Mass Concentration [g L ]

-1

= 0.43 = 0.71

0.02

[b]

1.5

= 0.00 = 0.14


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 41

= 1.00

0.01

= 0.43

1.0

= 0.71 = 1.00

0.5 0.10

0.05

0.00

0.00 1

10

2

10

3

10

4

10

5

1

10

10

100

Degree of Polymerization [-]

-1

Molecular Weight [g mol ]

Figure 4: SEC results of run 1 for the MWD [a] and DPD [b] at time 0 (black), 60(blue), 180(red), 300(gray) and 420 min(cyan) where θ is the ratio of individual time (min) to the total experiment time (420 min).

Results and Discussion Experimental part The degradation experiments were done for three different 5 g L−1 Kraft lignin samples that differ in terms of average MW and polydispersity (D). The SEC data for the degradation experiments is simplified by averaging this data as a function of the degree of polymerization of lignin. This is done by identifying a monomer unit for lignin. However, lignin is known to be a heterogeneous polymer that is based on different repeated units, which are guaiacyl (C10 H12 O3 ), syringyl (C11 H14 O4 ) and p-hydroxyphenol (C9 H10 O2 ). Additionally, the degradation of lignin can produce a wide product spectrum; starting from aromatics such as vanillin and vanillic acid (152-168 g mol−1 ) to a different variation of organic acids. 5 These products are difficult to quantify due to analytical limitations and the continued product degradation in the batch reactor. As a first model assumption, we consider the lignin to be based on a unique monomer. Assuming that lignin can be modelled by a virtual monomer of syringyl (C11 H14 O4 )N , the monomeric molecular weight is 210 g mol−1 . This infers that

12


Page 13 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


any component with MW less than 210 g mol−1 is a content of the products family that is called a virtual monomer. Subsequently, the mass concentration versus MW results were converted to be mass concentration versus DP, which is the degree of polymerization distribution (DPD). Figure 4 a and b shows the MWD and DPD, respectively, for the data points of the experiment run 1. For conventional polymer degradation, the distribution shifts to the low MW region. However, lignin is degraded differently showing two reaction time periods. First, there is a shift of the distribution to the right (high MW) in the first 180 min which is about 1/3rd of the reaction time. The second reaction time zone is contributed mainly by the depolymerization hence the distribution is shifting to the left. This observation suggests that there is a slight degree of cross-linking of lignin chains during the experiment, which was explained in the review by Rinaldi et al. For the process of Kraft lignin, more than half of the bonds in the raw lignin are β−O−4 bonds, which give the raw lignin a linear structure. β−O−4 is a β−ether bond that has a binding energy about 65 kcal mol−1 . The Kraft process selectively cleaves this linkage and results in C−C linkages via phenolic condensation and radical coupling. This cross-linking network generates the three-dimensional structure of lignin. Only one-seventh of the β−O−4 remains in the produced Kraft lignin which can probably explain the continuous increase in the average MW that takes place mainly in the first time period of the reaction. However, SEC analysis is based on size of the molecules which elutes at different time. Each elution time is subsequently related to a molecular weight based on a calibration curve. Therefore, a possible swelling of the macromolecules can lead to a change of steric hindrance without affecting the real molecular weight. This phenomenon presumably explains the apparent polymerization observed in the first hours of electrochemical process. In order to simulate this behavior in the model, the random chain scission is assumed to be a reversible reaction as follows: K

R A(x0 ) ←−→ A(x) + A(x0 − x)

Kr

13



Page 14 of 41

Table 1: Input and model parameters for the three different samples of lignin for the three runs. Input Parameters

Run 1 Run 2 Run 3

Maximum DP (L)

4543

4524

4517

705

683

545

Weight-average MW [ g mol ]

5416

4922

5735

Polydisprisity (D)

7.7

7.2

10.5

Model Parameter

Run 1 Run 2 Run 3

Number-average MW [ g mol−1 ] −1

Chain-end degradation rate constant [min−1 ] −1

Random degradation rate constant [min ]

2.9

2.6

3.1

0.22

0.21

0.24

1.1

1.3

Random recombination rate constant [min−1 ] 1.2

Modelling part The reaction kinetics model was done in MATLAB R2014a using the ode15s solver. The model needs first the input parameters to express the DPD that it estimates. These input parameters are tabulated in Table 1. In addition, to fit the kinetics model with the experimental results, it was assumed that the reaction rate coefficient for the random chain scission (KR ) is slightly dependent on the DP with a power of 0.1 while it is independent for the chain-end scission (KCE ) and random recombination (Kr ). In order to have an automated tool that can allow an easy way to predict the reaction kinetics, the reaction rate constant (k) has to be a function of certain input parameters. The rate constant for every reaction is found to be empirically related by the initial value of Mw and D. A linear relationship of the reaction rate constant with Mw and D, at time 0, was noticed. The empirical formula of the rate constant as a function of D and Mw and the level of confidence, for every run, are tabulated in Table 2. The model works with these empirical formulas regardless of the initial lignin heterogeneity. The rate constants for the three runs are shown in the model parameters in Table 1 and Figure S1. During the electrochemical reaction, it has been noticed that there is a change in the behavior of the reaction. From the first reaction time zone (first 180 min) and the second time 14


Page 15 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2: Linear relation (Eq.) of the reaction rate constants with Mw and D and the level of confidence (R2 ). Rate

Wight average MW

Polydisprisity

constant

(Mw )

(D)

kCE = 0.0006Mw - 0.2332 (5)

kCE = 0.1228D + 1.8172 (6)

0.9848

0.8551

kCE

Eq. R

kR kr

2

Eq.

kR =0.00003Mw + 0.0529 (7) kR = 0.0068D + 0.1662 (8)

R2

0.9847

0.8552

Eq.

kr = 0.0002Mw - 0.098 (9)

kr = 0.0516D + 0.7632 (10)

0.9848

0.8551

R

2

zone (after 180 min), a fixed rate constant cannot fit the experimental data. This behavior change is noticed by the shift of the MWD to the right (high MW) in the first reaction time zone. After that, the MWD shifts to the left (low MW) with less product formation rate. To take this effect into account, we defined the contribution factor. The contribution factor accounts for the influence of every reaction mechanism (random scission, random recombination and chain-end scission) in the overall reaction duration that is summarized in Table 3. The contribution factor gives the model flexibility to cope with the unique behavior of the lignin degradation, which is likely caused by the change in the amorphicity of lignin with time, as explained previously. The first time zone is dominant equivalently by the chain-end and the random scissions with 35% and 43%, respectively. Additionally, a contribution factor of 22% is contributed by the random recombination. In the second time zone, random scission is more dominant which is physically indicated by the broadness of the overall DPD. Based on our assumption that the random scission is accompanied with a reversible random recombination, the recombined C−C linkages tend to have similar binding energy. Therefore, there is an equally probability for these bonds to be cleaved randomly. The values of the contribution factor were determined by using the ”nonlinear least-squares curve-fitting” in MATLAB which is multiplied by the rate constants to give the best fitting. It is a unique solution and the sum of the contribution factor values for every reaction time 15



zone is defined to be equal to 1. This engineering solution allows for the model to fit the experimental data with a standard error of ± 0.01 g L−1 , but it needs further chemical elucidation beyond the scope of this paper. Table 3: contribution factor for the three reaction mechanisms the random scission (kR ), random recombination (kr ) and chain-end (kCE ) scission. Rate constant 0-180 [min]

180 - 420 [min]

kCE

0.345 ± 0.005 0.065 ± 0.020

kR

0.425 ± 0.025 0.870 ± 0.050

kr

0.235 ± 0.025 0.045 ± 0.040

The discrepancy between the feed characteristics for the three runs, gives a better confidence in the prediction of the model and how it fits the experiment data. Figure 5a shows the product (monomer) formation with time. The experiment data presented a high product formation rate in the first 180 min of the reaction time. This result supports the initial assumption that the monomer is produced mainly by the chain-end scission and slightly by the random scission. However, due to the fact that lignin has no unique monomer, the chain-end scission is actually producing a random set of components that falls in the specified MW range of the virtual monomer. Furthermore, it is even more significant that the model can also predict the overall degree of polymerization distribution (DPD) with time. Figure 5b displays the prediction of the number average DP which can demonstrate the two time zones of the degradation. In the first 180 min of the reaction, degraded lignin can maintain its average molecular weight due to the random recombination effect. Similarly, the resulted DPD evolution with time is indicated in Figure 5c, d, e, and f where the modeled DPD shifted in the same manner as the experimental DPD. Despite the good results that the model is generating, there are several improvements to be addressed in the future. Because of the limitation in analyzing the product composition, the model assumes that there is only one product (monomer) formed. If the product breakdown can be analyzed, several products can be added to the model and better un16


Page 16 of 41

Page 17 of 41

35

[a]

Number Average DP [-]

-1


2.0

1.5

Exp.

1.0 Model

0.5

0

100

200

300

400

[b]

30 Model

25 20

Exp.

15 10 5

0.0

0

100

Time [min]

[c]

300

400

[d]

-1


0.10

-1


200

Time [min]

0.10

0.08 Model

0.06

Exp.

0.04

0.02

0.00

0.08

Model

0.06

0.04 Exp.

0.02

0.00 10

100

10


100


[f]

[e]

0.10

Model

-1

-1


0.10


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Model

0.08 Exp.

0.06

0.04

0.02

0.00

Exp.

0.08

0.06

0.04

0.02

0.00 10

100

10


100


Figure 5: Experiment and model results for the product formation [a] the number average DP [b] and the evolution of lignin DPD for time 60 [c], 180 [d], 300 [e] and 420 min [f], respectively.

17



derstanding of the kinetics is obtained. Furthermore, a product degradation kinetics can be incorporated into the model which is essential for investigating the optimum reaction residence time. Additionally, the effect of the voltage was lumped in the electrochemical reaction rate coefficient because it is set to be constant while it is supposed to be a key parameter for the rate coefficient. Moreover, other reaction conditions can be added in the model, such as the type of lignin, solvent, electrode material, reactor life time, temperature, current and pressure, by studying the design of the experiment where the weight for every factor is identified. As a result, it is possible to generate a comprehensive, but complicated, kinetics model. Yet, the methodology presented here may also be valuable in other areas such as water treatment where natural organic matter needs to be degraded and insights into the mechanisms are still required. 50

Conclusions and Outlook Lignin depolymerization kinetics as a function of random scission, random recombination and chain-end scission emulated experimental results with a high degree of similarity. This was done by introducing the contribution factor for every reaction, which is related to the unique phenomenon of lignin degradation. The increment of Mn at the beginning of the electrochemical reaction and then the decrease were considered in the model by adjusting the contribution factor to validate the experiment results. Fitting the model to the experimental data indicates the dependency of the reaction rate coefficient with the DP and the rate constant values, which have a linear relationship with the initial value of D and Mw . The model defines the reaction kinetics as a population balance for the concentration of every degree of polymerization in either a discrete solution for the low MW or a continuous solution for the high MW. Therefore, a set of PBEs were solved for every reaction simultaneously using MATLAB without any considerable computational time. The model results of the lignin distribution and product formation with time behave in a similar manner to the

18


Page 18 of 41

Page 19 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


actual experiment results though the lignin samples for every run are different. Further modifications can be made to the model by identifying the list of the products and their degradation kinetics, however, this requires improving the analytical method to measure these products.

Supporting information The Supporting information is available free of charge on the ACS Publications website at DOI: The detail derivation of the governing equations and the mathematical solution; Value r e (stoichiometric (stoichiometric Kernel) for chain-end scission (Table S1); Value of qi,j of qi,j

Kernel) for random scission and recombination (Table S2); Variation during the depolymerization reaction of temperature, current and power (Table S3); Linear relationship of reaction rate constants and initial values of Mw and polydispersity, respectively (Figure S1).

Author’s information Corresponding Author: Prof. Matthias Wessling E-mail: [email protected]

Note The authors declare no conflict of interests.

Acknowledgement The authors appreciate the financial support of Saudi Arabia Basic Industries Corporation (SABIC) and of the Marie Curie Action in the framework of SuBiCat (FP7) EU Marie Curie

19



project (PITN-GA-2013-607044). We thank Rainer Haas for the SEC measurements and Hanna Brings and Vadim Aniko for their support in the experiments.

Abbreviations/nomenclatures λ

Degree of dependency of the rate coefficient on MW

θ

Time ratio with respect to the total experiment time (420 min)

A(x0 )

Polymer before degradation

A(x)

Resulted polymer from random scission

A(x0 − x)

Resulted polymer from random scission

A(xi )

Specific product

A(x0 − xi )

Resulted polymer from chain-end scission

b

DP boundary

b+L

Maximum DP

kR

Random scission rate constant [min−1 ]

kCE

Chain-end scission rate constant [min−1 ]

kr

Random recombination rate constant [min−1 ]

KR

Rate coefficient for random scission [DP0.1 min−1 ]

KCE

Rate coefficient for chain-end scission [min−1 ]

Kr

Rate coefficient for random recombination [min−1 ]

L

Chain length

Mn

Number average MW [ g mol−1 ]

Mw

Weight average MW [ g mol−1 ]

n(x, t)

Population of particle in size x

Q(x, x0 )

Stoichiometric kernel

r

Geometric ratio

v

Pivot DP

x

Molecular weight or degree of polymerization [ g mol−1 ] 20


Page 20 of 41

Page 21 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


xi

Product MW or DP

x0

Polymer MW or DP

xm

Monomer DP

D

Polydispersity

DP

Degree of polymerization

DPD

Degree of polymerization distribution

Eq.

Linear relation of the reaction rate constants with Mw and D

FP

Fixed Pivot

MW

Molecular weight [ g mol−1 ]

MWD

Molecular weight distribution

PBE

Population balance equations

R2

Level of confidence

SEC

Size exclusion chromatography

References (1) Ragauskas, A. J. et al. Lignin valorization: improving lignin processing in the biorefinery. Science 2014, 344, 709–+, DOI: 10.1126/science.1246843. (2) Zakzeski, J.; Bruijnincx, P. C.; Jongerius, A. L.; Weckhuysen, B. M. The catalytic valorization of lignin for the production of renewable chemicals. Chem. Rev. 2010, 110, 3552–3599, DOI: 10.1021/cr900354u. (3) Gasson, J. R.; Forchheim, D.; Sutter, T.; Hornung, U.; Kruse, A.; Barth, T. Modeling the lignin degradation kinetics in an ethanol/formic acid solvolysis approach. Part 1. Kinetic model development. Ind. Eng. Chem. Res. 2012, 51, 10595–10606, DOI: 10.1021/ie301487v. (4) Di Marino, D.; Stöckmann, D.; Kriescher, S.; Stiefel, S.; Wessling, M. Electrochemical

21



Page 22 of 41

depolymerisation of lignin in a deep eutectic solvent. Green Chem. 2016, 18, 6021–6028, DOI: 10.1039/C6GC01353H. (5) Stiefel, S.; Marks, C.; Schmidt, T.; Hanisch, S.; Spalding, G.; Wessling, M. Overcoming lignin heterogeneity: reliably characterizing the cleavage of technical lignin. Green Chem. 2016, 18, 531–540, DOI: 10.1039/C5GC01506E. (6) Schmitt, D.; Regenbrecht, C.; Hartmer, M.; Stecker, F.; Waldvogel, S. R. Highly selective generation of vanillin by anodic degradation of lignin: a combined approach of electrochemistry and product isolation by adsorption. Beilstein J. Org. Chem. 2015, 11, 473, DOI: 10.3762/bjoc.11.53. (7) Parpot, P.; Bettencourt, A.; Carvalho, A.; Belgsir, E. Biomass conversion: attempted electrooxidation of lignin for vanillin production. J. Appl. Electrochem. 2000, 30, 727– 731, DOI: 10.1023/A:1004003613883. (8) Tolba, R.; Tian, M.; Wen, J.; Jiang, Z.-H.; Chen, A. Electrochemical oxidation of lignin at IrO2-based oxide electrodes. J. Electroanal. Chem 2010, 649, 9–15, DOI: 10.1016/j.jelechem.2009.12.013. (9) Reichert, E.; Wintringer, R.; Volmer, D. A.; Hempelmann, R. Electro-catalytic oxidative cleavage of lignin in a protic ionic liquid. Phys. Chem. Chem. Phys. 2012, 14, 5214–5221, DOI: 10.1039/C2CP23596J. (10) Dier, T. K.; Rauber, D.; Durneata, D.; Hempelmann, R.; Volmer, D. A. Sustainable electrochemical depolymerization of lignin in reusable ionic liquids. Sci. Rep. 2017, 7, 5041, DOI: 10.1038/s41598-017-05316-x. (11) Di Marino, D.;

Aniko, V.;

Stocco, A.;

Kriescher, S.;

Wessling, M. Emul-

sion electro-oxidation of kraft lignin. Green Chem. 2017, 19, 4778–4784, DOI: 10.1039/C7GC02115A.

22


Page 23 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(12) Stiefel, S.; Lölsberg, J.; Kipshagen, L.; Möller-Gulland, R.; Wessling, M. Controlled depolymerization of lignin in an electrochemical membrane reactor. Electrochem. Commun. 2015, 61, 49–52, DOI: 10.1016/j.elecom.2015.09.028. ˇ (13) Zabkov´ a, M.; da Silva, E. B.; Rodrigues, A. Recovery of vanillin from lignin/vanillin mixture by using tubular ceramic ultrafiltration membranes. J. Membr. Sci. 2007, 301, 221–237, DOI: 10.1016/j.memsci.2007.06.025. (14) McCoy, B. J.; Madras, G. Degradation kinetics of polymers in solution:

dy-

namics of molecular weight distributions. AlChE J. 1997, 43, 802–810, DOI: 10.1002/aic.690430325. (15) Kiparissides, C. Challenges in particulate polymerization reactor modeling and optimization: A population balance perspective. J. Process Control 2006, 16, 205–224, DOI: 10.1016/j.jprocont.2005.06.004. (16) Laurence, R.; Galvan, R.; Tirrell, M. Polymer Reactor Engineering; Springer, 1994; pp 87–124, DOI: 10.1007/978-94-011-1338-0_3. (17) Feinberg, M. Chemical reaction network structure and the stability of complex isothermal reactorsI. The deficiency zero and deficiency one theorems. Chem. Eng. Sci. 1987, 42, 2229–2268, DOI: 10.1016/0009-2509(87)80099-4. (18) Sterling, W. J.; McCoy, B. J. Distribution kinetics of thermolytic macromolecular reactions. AlChE J. 2001, 47, 2289–2303, DOI: 10.1002/aic.690471014. (19) Wang, M.; Smith, J.; McCoy, B. J. Continuous kinetics for thermal degradation of polymer in solution. AlChE J. 1995, 41, 1521–1533, DOI: 10.1002/aic.690410616. (20) Guaita, M.; Chiantore, O.; Luda, M. P. Monte Carlo simulations of polymer degradations. I: Degradations without volatilization. Macromolecules 1990, 23, 2087–2092, DOI: 10.1021/ma00209a035. 23



(21) McDermott, J.; Klein, M. Chemical and probabilistic modelling of complex reactions: A lignin depolymerization example. Chem. Eng. Sci. 1986, 41, 1053–1060, DOI: 10.1016/0009-2509(86)87192-5. (22) Staggs, J. Modelling end-chain scission and recombination of linear polymers. Polym. Degrad. Stab. 2004, 85, 759–767, DOI: 10.1016/j.polymdegradstab.2004.01.021. (23) Bose, S. M.; Git, Y. Mathematical modelling and computer simulation of linear polymer degradation: Simple scissions. Macromol. Theory Simul. 2004, 13, 453–473, DOI: 10.1002/mats.200300036. (24) Nattorp, A.; Graf, M.; Sp¨ uhler, C.; Renken, A. Model for random hydrolysis and end degradation of linear polysaccharides: Application to the thermal treatment of mannan in solution. Ind. Eng. Chem. Res. 1999, 38, 2919–2926, DOI: 10.1021/ie990034j. (25) Kumar, S.; Ramkrishna, D. On the solution of population balance equations by discretization−I. A fixed pivot technique. Chem. Eng. Sci. 1996, 51, 1311–1332, DOI: 10.1016/0009-2509(96)88489-2. (26) Kumar, S.; Ramkrishna, D. On the solution of population balance equations by discretizationII. A moving pivot technique. Chem. Eng. Sci. 1996, 51, 1333–1342, DOI: 10.1016/0009-2509(95)00355-X. (27) Kumar, S.; Ramkrishna, D. On the solution of population balance equations by discretizationIII. Nucleation, growth and aggregation of particles. Chem. Eng. Sci. 1997, 52, 4659–4679, DOI: 10.1016/S0009-2509(97)00307-2. (28) Griggs, A. J.; Stickel, J. J.; Lischeske, J. J. A mechanistic model for enzymatic saccharification of cellulose using continuous distribution kinetics I: depolymerization by EGI and CBHI. Biotechnol. Bioeng. 2012, 109, 665–675, DOI: 10.1002/bit.23355.

24


Page 24 of 41

Page 25 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(29) Stiefel, S.; Schmitz, A.; Peters, J.; Di Marino, D.; Wessling, M. An integrated electrochemical process to convert lignin to value-added products under mild conditions. Green Chem. 2016, 18, 4999–5007, DOI: 10.1039/C6GC00878J. (30) Ho, Y. K.; Doshi, P.; Yeoh, H. K.; Ngoh, G. C. Modeling chain-end scission using the Fixed Pivot technique. Chem. Eng. Sci. 2014, 116, 601–610, DOI: 10.1016/j.ces.2014.05.035. (31) Madras, G.; Chung, G.; Smith, J.; McCoy, B. J. Molecular weight effect on the dynamics of polystyrene degradation. Ind. Eng. Chem. Res. 1997, 36, 2019–2024, DOI: 10.1021/ie9607513. (32) Vanholme, R.; Demedts, B.; Morreel, K.; Ralph, J.; Boerjan, W. Lignin biosynthesis and structure. Plant Physiol. 2010, 153, 895–905, DOI: 10.1104/pp.110.155119. (33) Stickel, J. J.; Griggs, A. J. Mathematical modeling of chain-end scission using continuous distribution kinetics. Chem. Eng. Sci. 2012, 68, 656–659, DOI: 10.1016/j.ces.2011.09.028. (34) Kostoglou, M. Mathematical analysis of polymer degradation with chain-end scission. Chem. Eng. Sci. 2000, 55, 2507–2513, DOI: 10.1016/S0009-2509(99)00471-6. (35) Kostoglou, M.; the

breakage

Karabelas, A. On sectional techniques for the solution of equation.

Comput.

Chem.

Eng.

2009,

33,

112–121,

DOI:

10.1016/j.compchemeng.2008.07.002. (36) Prasad, G.; Agnew, J.; Sridhar, T. Modeling of coal liquefaction kinetics based on reactions in continuous mixtures. Part II: Comparison with experiments on catalyzed and uncatalyzed liquefaction of coals of different rank. AlChE J. 1986, 32, 1288–1300, DOI: 10.1002/aic.690320807.

25



Page 26 of 41

(37) Madras, G.; Kumar, S.; Chattopadhyay, S. Continuous distribution kinetics for ultrasonic degradation of polymers. Polym. Degrad. Stab. 2000, 69, 73–78, DOI: 10.1016/S0141-3910(00)00042-2. (38) Sivalingam, G.; Agarwal, N.; Madras, G. Distributed midpoint chain scission in ultrasonic degradation of polymers. AlChE J. 2004, 50, 2258–2265, DOI: 10.1002/aic.10185. (39) Staggs, J. A continuous model for vapourisation of linear polymers by random scission and recombination. Fire Saf. J. 2005,

40,

610–627,

DOI:

10.1016/j.firesaf.2005.05.004. (40) Madras, G.; Smith, J.; McCoy, B. J. Effect of Tetralin on the Degradation of Polymer in Solution. Prepr. Pap. - Am. Chem. Soc., Div. Fuel Chem. 1995, 40, 628–628, DOI: 10.1021/ie00039a010. (41) McCoy, B. J. Continuous-mixture kinetics and equilibrium for reversible oligomerization reactions. AlChE J. 1993, 39, 1827–1833, DOI: 10.1002/aic.690391110. (42) McCoy, B. J.; Wang, M. Continuous-mixture fragmentation kinetics: particle size reduction and molecular cracking. Chem. Eng. Sci. 1994, 49, 3773–3785, DOI: 10.1016/0009-2509(94)00172-3. (43) Madras, G.; McCoy, B. J. Time evolution to similarity solutions for polymer degradation. AlChE J. 1998, 44, 647–655, DOI: 10.1002/aic.690440313. (44) Staggs, J. Discrete bond-weighted random scission of linear polymers. Polymer 2006, 47, 897–906, DOI: 10.1016/j.polymer.2005.11.085. (45) Madras, G.; Karmore, V. Evolution to similarity solutions for polymerization and depolymerization with microwave radiation. Polym. Int. 2001, 50, 1324–1330, DOI: 10.1002/pi.779. 26


Page 27 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(46) Madras, G.; McCoy, B. J. Oxidative degradation kinetics of polystyrene in solution. Chem. Eng. Sci. 1997, 52, 2707–2713, DOI: 10.1016/S0009-2509(97)00091-2. (47) Wang, M.; Zhang, C.; Smith, J.; McCoy, B. J. Continuous-Mixture kinetics of thermolytic extraction of coal in supercritical fluid. AlChE J. 1994, 40, 131–142, DOI: 10.1002/aic.690400115. (48) Aris, R.; Gavalas, G. R. On the theory of reactions in continuous mixtures. Philos. Trans. R. Soc. London, Ser. A 1966, 260, 351–393, DOI: 10.1098/rsta.1966.0054. (49) Vanni, M. Approximate population balance equations for aggregation–breakage processes. J. Colloid Interface Sci. 2000, 221, 143–160, DOI: 10.1006/jcis.1999.6571. (50) Jansen, R. H. S.; Zwijnenburg, A.; van der Meer, W. G. J.; Wessling, M. Outside-In Trimming of Humic Substances During Ozonation in a Membrane Contactor. Environ. Sci. Technol. 2006, 40, 6460–6465, DOI: 10.1021/es060533t.

27



Graphical TOC Entry

Population balance equations are used to model the kinetics of lignin depolymerization leading to a better prediction of sustainable products.

28


Page 28 of 41

Page 29 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Continuos (Moment Method)


Reaction Kinetics NonConventional

Conventional (Chemical Reaction Network)

(MWD or PCLD)

Deterministic Approach (PBE)

Discrete

Statistical Approach (Probabilitis)

Discretecontinuous transformation

Direct Approach


Markov chain theory

Recursive method (Binary Tree)

ACS Sustainable Chemistry & Engineering 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41


Page 30 of 41

Page 31 of 41


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60




Page 32 of 41

Page 33 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60





Page 34 of 41

Page 35 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60





Page 36 of 41

Page 37 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60




[b ]

1 .5

θ= θ= θ= θ= θ=

M a s s C o n c e n tr a tio n

[g L

-1

]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Page 38 of 41

1 .0 0 .5 0 .1 0

0 .0 5

0 .0 0 1

1 0 ACS Paragon Plus Environment

1 0 0

D e g r e e o f P o ly m e r iz a tio n [- ]

0 .0 0 .1 0 .4 0 .7 1 .0

0 4 3 0

1

Page 39 of 41

ACS Sustainable Chemistry & Engineering Model

Reaction

Lignin Feed

1 2 3 4 5 6 7 Degree of Polymerization [-] 8 𝑑𝑝 𝑥, 𝑡 9 𝑑𝑡 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

-1


-1


0.08

Ni-wire

0.06 0.04

Lignin

0.02 0.00

10

Model

0.10

0.10

Experiment

0.08 0.06 0.04

Lignin

0.02 0.00

10

100

100

Degree of Polymerization [-] ∞

= – 𝑘 𝑥 𝑝 𝑥, 𝑡 + 2 න 𝑘 𝑥΄ 𝑝 𝑥΄, 𝑡 𝜈 𝑥, 𝑥΄ 𝑑𝑥΄ 𝑥



Model

Reaction

Lignin Feed

Model

-1


0.10

Ni-wire

-1


1 2 3 4 5 6 0.10 7 8 9 0.08 10 11 12 0.06 13 14 15 0.04 16 17 18 19 0.02 20 21 22 0.00 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Page 40 of 41

Lignin

10

100


∞ 𝑑𝑝 𝑥, 𝑡 = – 𝑘 𝑥 𝑝 𝑥, 𝑡 + 2 න 𝑘 𝑥΄ 𝑝 𝑥΄, 𝑡 𝜈 𝑥, 𝑥΄ 𝑑𝑥΄ 𝑑𝑡 𝑥


Experiment

0.08 0.06 0.04

Lignin

0.02 0.00

10

100


Page 41 of 41


0 .0 3

[a ]

]

θ= θ= θ= θ= θ=

M a s s C o n c e n tr a tio n [g L

-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

0 .0 2

0 .0 1

0 .0 0 .1 0 .4 0 .7 1 .0

0 .0 0 1 0

1

1 0

2

1 0

3


1 0

4

1 0 -1

M o le c u la r W e ig h t [g m o l ]

5

0 4 3 0

1

Unravelling Electrochemical Lignin Depolymerization - ACS Publications

Recommend Documents