Residence time distribution, a simple tool to understand the behaviour ofpolymeric mini-flow reactors

Victor Sans,*ab Naima Karbass,a M. Isabel Burguete,a Eduardo Garcıa-Verdugo*a and Santiago V. Luisa

Received 10th May 2012, Accepted 13th July 2012

DOI: 10.1039/c2ra20903a

A simple method for the determination of the residence time distribution (RTD) of different polymer-

based mini-flow reactors has been developed. The flow patterns have been adjusted employing the

axial dispersion model, allowing a quantitative comparison of the flow patterns of the different

structures. The use of different pulse tracer experiments highlights the differences in reactor

behaviour depending on the nature (gel vs. macroporous) and shape (beads vs. monoliths) of the

polymeric materials used in the reactor preparation. Thus, reactors based on monolithic columns

showed a superior performance in terms of flow distribution when compared to commercial bead-

shaped packed polymers of different sizes and backbone structure, confirming previous experimental

results. These differences can help to understand the different catalytic efficiency detected for these

mini-flow fixed-bed reactors. The model presented can help to properly design new processes based

on the use of continuous flow reactors facilitated by functional materials, which is becoming an

essential goal nowadays, in particular in the context of developing new efficient and clean

technologies.

Introduction

The synthesis of organic molecules by the application of so-

called flow chemistry has gained a great deal of attention in

recent years, due to its inherent higher efficiency compared to

traditional batch processes.1 Although some nice examples of

flow organic synthesis have been reported in the homogeneous

phase,2 the synergetic combination of continuous-flow and

heterogeneous reagents, catalysis and scavengers represents a

very efficient strategy for both the development of simple organic

synthetic transformations and the preparation of small complex

molecules of pharmaceutical relevance.3–5 Furthermore, the

combination of these tools with other facilitating techniques

(the use of neoteric solvents, microwave, sonochemistry, etc.) has

led to the development of new green and more efficient synthetic

processes.6

The potential of solid-supported reagents, scavengers and

catalysts for developing flow processes has been realized as one

of their key properties.1,3,7 The matrices used as the supports can

be classified, according to their nature, into organic and

inorganic. Most of the work carried out has concentrated on

the use of two relatively simple polymeric networks: cross-linked

polystyrene and polyacrylic derivatives. Alternatively, functio-

nalised inorganic materials obtained either by modification of

different oxides or by sol–gel processes have also been

successfully used.8 In this way, the joint efforts of synthetic

and materials chemists and chemical engineers have resulted in

the development of continuous flow devices and microreactors,

which allow the rapid preparation of compounds with minimum

workup9 and facilitate both automation and fast operational

optimisation.10

Different reactor configurations have been assayed to design

flow processes attending to the type and shape of the material

employed. Among them, some non exhaustive examples can be

mentioned: micrometre-sized open tubes with catalytic moieties

grafted on the walls,11 packed-bed reactors,1,7 and monolithic

reactors.12–14 The selection of the reactor configuration can lead,

in some cases, to significant differences in performance. Thus,

for instance, a recent report by Coq and coworkers addressed the

use of hierarchical silica monoliths grafted with acidic and basic

moieties as continuous flow reactors for catalysis. Processes

based on the monolithic reactors proved to be 2 to 10 folds more

productive than packed-bed or batch-mode reactors in two

different model reactions: Knoevenagel condensation and

transesterification.15 McQuade and coworkers pointed out the

importance of the nature of the support to develop a pressure-

driven system by passing different solvents through a packed-bed

reactor and qualitatively assessing whether the flow was free or

constricted.16 Typically, gel-type lightly crosslinked resins only

swell in certain solvents, which allows a proper flow through the

microchannels of the resin (usually beads) exclusively in the

presence of the proper swelling solvent. Nevertheless, the

swelling is accompanied by a change in volume that can be very

important, thus affecting the packing. Highly cross-linked or

aDepartment of Inorganic and Organic Chemistry, University JaumeI/CSIC, Avda. Sos Baynat s/n, E-12071, Castellon, Spain.E-mail: eduardo.garcia-verdugo@qio.uji.esbSchool of Chemistry, University of Glasgow, G12 8QQ, Glasgow, UK.E-mail: victors@chem.gla.ac.uk

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macroreticular resins and silicas, on the other hand, allow

optimal flow conditions, close to plug-flow, under nearly all

solvent conditions as they do not appreciably swell, thus not

producing changes in the packing. There are also significant

differences between the fixed-bed reactors, packed either with

beads or monolithic polymeric materials, when they are used for

both synthesis and separation processes. Thus, employing a

simple method for understanding and controlling the variables

governing the flow distribution is of the greatest interest.17 Here,

different mini-flow packed-bed reactors, which were prepared

using different types of cross-linked polymers (gel-type, macro-

porous beads and macroporous monoliths), have been char-

acterized by means of residence time distribution (RTD) studies

using simple pulse tracer experiments. The flow patterns allow

the understanding of the different catalytic efficiencies observed

for the mini-flow reactors used in C–C coupling reactions.

Experimental

Monolithic mini-flow reactors 1 and 2 (Mfr-1 and Mfr2)

Monolithic reactors based on PS–DVB (polystyrene-divinylben-

zene) polymers were prepared by the polymerisation of different

polymer mixtures, using a previously reported methodology.18 The

compositions selected (Table 1) allowed us to obtain monoliths with

different ranges of porosity and pore size (see Table 1).

Mini-flow reactor 3 (Mfr-3)

This reactor was prepared by packing a commercial macropor-

ous Merrifield resin obtained in the form of beads. A chloride

loading of 1.2 mmol Cl g21 and a DVB content of ca. 55% DVB

was obtained by means of Raman spectroscopy.19 The bead size

was estimated to be 70.4 mm with a standard deviation of 12.7

mm. This material was packed in a 15 cm stainless steel column

with a 1/4 inch internal diameter similar to the one used for the

preparation of Mfr-1 and Mfr-2. The void volume was

determined by filling the empty space with a known solvent

(THF). In this way, the porosity was found to be 0.74.

Mini-flow reactor 4 (Mfr-4)

This reactor was prepared by packing an Amberlite resin IR-200

in the Na+ form in a 15 cm stainless steel column with a 1/4 inch

internal diameter as before. The average bead size was 534.85 mm

with a standard deviation of 127.21 mm.

Mini-flow reactor 5 (Mfr-5)

This reactor was prepared by packing a commercial gel-type

Merrifield resin (4.3 mmol g21, 1% crosslinked) in a glass column

(10 6 100 mm, with an adjustable volume from 1–10 mL). Thus,

half of the column (5 mL) was filled with the polymer. When the

resin was wetted with the different solvents (toluene or

acetonitrile (ACN)), the volume of the reactor was adjusted to

the volume occupied by the swollen resin.

PdNPs–SILLP (PalladiumNanoParticles–Supported-Ionic-

Liquid-Like-Phases) reactors

Mini-flow reactors PdNPs–SILLP-1 and PdNPs–SILLP-2 were

prepared by modification of the mini-flow reactors Mfr-1 and

Mfr2 and tested in the Heck reaction in hot pressurised ethanol

as previously reported.20 In a similar way, the PdNPs–SILLP-3

mini-flow reactor was also prepared by the modification of the

corresponding Mfr-3 reactor.

Pulse tracer experiments

All the experiments were carried out using the set-up shown

schematically in Fig. 1, using a Hitachi HPLC pump, a fixed

Table 1 Copolymerization conditions and characterisation of monolithic mini-flow reactors

Mini-flow reactor ClVB (%)a DVB (%)a rap (g cm23)c d50 (mm)d pore volume (cm3 g21) eoe

Mfr-1b 16 24 0.367 0.39 1.8694 0.69Mfr-2b 12 18 0.378 4.69 1.6383 0.62a Expressed as % weight of the polymerisation mixture. b Toluene:dodecanol 1 : 4 was used as the porogenic mixture. Co-polymerization wasinitiated by AIBN and carried out at 70 uC using a 2 : 3 weight ratio monomeric mixture–porogen, inside AISI 316 tubing of 15 cm length and 1/4din. c Apparent density: massmaterial/densitymaterial.

d Diameter at 50% of pore size distribution. e Open porosity: void volume/total volume.

Fig. 1 The schematic experimental set-up for the RTD studies.

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wave length UV-visible detector and a Rheodyne injection valve

with a 50 ml loop. All the connections were made with 1/16

HPLC tubing to try to minimize the dead volume. The tracer

used was toluene, although for the experiments performed in

toluene as the solvent, nitrobenzene was used as tracer. The

reactors were prepared using either a 10 mL Omnifit glass (10 6100 mm) or stainless steel columns (5 cm length and 0.4 cm

diameter). Flow rates ranging from 0.1 to 3 mL min21 were

investigated with the use of acetonitrile as the solvent in most

cases. Monolithic columns were limited to a maximum flow of

2.5 mL min21 to avoid overpressures, which could damage the

columns. The variation of the tracer with time was determined

by UV-vis detection at 224 nm for toluene and at 240 nm when

nitrobenzene was used as the tracer.

C–C coupling reaction under flow conditions

The reaction of iodobenzene with methyl acrylate was examined in a

continuous flow system using hot pressurized ethanol as the solvent.

A solution of iodobenzene and methyl acrylate (0.67 mol L21 in

EtOH, 1 : 1.1 : 2 molar ratio iodobenzene : methyl acrylate : Et3N)

was pumped at a flow rate of 0.2 mL min21 through the monolithic

reactor. Aliquots were taken at regular time intervals and analyzed

by HPLC for the methylcinnamate content.

Results and discussion

In this work, packed-bed reactors, functionalized with either

polymeric beads or monoliths were used, as this is the easiest

approach towards the design of polymer assisted flow devices.

Three classical reactor designs, using this approach, have been

described in detail by Hodge.1,7b In this regard, the more

common configuration is based on the flow-trough packed-bed

reactors flowing either upwards or downwards using a pressure-

driven flow. Alternatively, the use of electrosmotic-driven flows

also allows continuous processes using a wider range of packing

materials.21 However, these systems are far more complex than

pressure-driven systems, being restricted to polar solvents.

Chloromethylated resins were selected as the starting poly-

meric materials as chloromethyl groups allow the easy introduc-

tion of a great number of reagents, scavengers and catalysts.22 A

wide range of flow processes have been developed with fixed-bed

reactors based on those materials. In principle, the flow patterns

of the fixed-bed reactors should not be significantly modified by

the introduction of such groups and the tools here reported will

also be applicable for mini-flow reactors packed with modified

resins. An example of those modified polymers should be the use

of supported ionic liquid like phases (SILLPs) prepared from

chloromethylated PS–DVB polymers for the immobilisation of

different types of catalysts.23 Thus, for instance, metal nano-

particles (MNPs) can be synthesised and stabilised by different

SILLPs.20,24 Those MNPs–SILLP composites can be used as the

packing material to prepare fixed-bed reactors. Indeed, SILLP

mini-flow reactors bearing PdNPs are able to efficiently catalyse

C–C coupling reactions between iodobenzene and methyl

acrylate using hot pressurized ethanol as the solvent (200 uCand 80 bars).20 However, as it is shown in Table 2, the catalytic

efficiency obtained for the different PdNP–SILLP mini-flow

reactors based on either monolithic or bead materials (entries 1

and 2 vs. 3) was significantly different (up to one order of

magnitude). Moreover small differences were found for the mini-

flow reactors based on PdNPs–SILLPs supported on monolithic

polymers prepared with slightly different compositions.25 RTD

studies may help us to rationalise such differences based on the

nature of the material employed to pack the corresponding fixed-

bed mini-flow reactors.

Residence time distribution (RTD) studies

The knowledge about the flow patterns inside a reactor is vital to

predict and explain the general behaviour of the reactor and the

above mentioned differences. Among the different possibilities

and from an engineering point of view, the residence time

distribution (RTD) of a reactor is one of the most informative

characterizations of the flow pattern in a chemical reactor.26 For

this reason, there have been numerous efforts to study the

residence time distribution inside vessels.27 The theory of RTD

was first proposed by MacMullin and Weber,28 and worked out

in more detail by Danckwerts some years later.29 It provides

information on how long the various elements have been in the

reactor.30 It is a quantitative measure of the degree of back

mixing within a system31 and allows for an accurate kinetic

modelling of the system helping to achieve or preserve a desired

flow pattern during reactor design. Besides, RTD allows for a

more thorough comparison between systems having different

configurations of the reactor, it is an extraordinarily simple tool

for a successful process scale-up. In general, the RTD of mini-

flow reactors can be determined by simple tracer experiments. In

these experiments, an inert tracer32 is injected into the solvent

stream flowing through the reactor vessel and its distribution is

analyzed, for instance by UV-vis, at the outlet, monitoring the

concentration of the tracer over time (see Fig. 1).29,33 In this way,

from the experimental curves obtained it is possible to calculate

the E(t) curve, the mean residence time (t) and the variance by

applying eqn (1)–(3):

E tð Þ~ C tð ÞÐ?

0

C tð Þ dt

(1)

t~

ð?

0

t:E tð Þ dt (2)

Table 2 Catalytic activity obtained for different mini-flow PdNPs-SILLPs catalytic reactorsa

Entry Fixed-bed material Pd loadinge Yield (%)f Productivityg

1 Monolithb 0.21 93 22.22 Monolithc 0.18 50 19.73 Beadsd 0.63 70 3.9a Reaction conditions: 200 uC and 80 bars; 0.2 mL min21; PhIconcentration 0.67 mmol L21; 1 : 1.1 : 2 PhI : methylacrylate : Et3Nratio; reactor size: 15 cm length 6 J inch internal diameter.b Prepared from Mfr-1. c Prepared from Mfr-2. d Prepared from Mfr-3.e mmol Pd g21 polymer calculated by ICP-MS. f Calculated by HPLCanalysis of samples collected at the reactor outlet. g (mol Product)?x(mol cat)21?x min21.

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s2~

Ð?

0

t-tð Þ2:C tð Þ dt

Ð?

0

C tð Þ dt

(3)

In order to facilitate the comparison of the results obtained for the

different mini-flow reactor configurations (involving, for instance,

different packings), it is convenient to employ dimensionless units:

h~t

t(4)

The mean liquid velocity has been calculated according to eqn

(5).33

uL~L

t(5)

Where L is the length of the mini-flow reactor.

E(t) curves as a qualitative tool to study the characteristics of gel-

type and macroporous polymer-packed reactors.

The nature, shape and morphology of the polymers are key

parameters to obtain a proper reactor design. In general, gel-type

resins are by far the most employed supports to develop polymer

supported systems, especially when batch processes are con-

sidered.22 By definition, gel-type resins do not possess any

permanent porosity and thus their swelling in an appropriate

solvent is required for any reaction to occur in the interior of the

beads.34 The selection of the solvent depends on the chemical

nature of the polymeric backbone and that of the functional

groups being introduced. Thus, for PS–DVB matrices solvents

like toluene or dichloromethane are very appropriate, while

more polar solvents are compatible with acrylic-derived resins.

In this regard, to design mini-flow reactors based on gel-type

polymers, it is essential that the packing will estimate the change

in volume that will take place by the swelling/shrinking of the

polymer with the solvent employed for the process. The need for

a proper adjustment of the reactor design has hampered the use

of gel-type resins for efficient flow processes many times.

However, if this increment in volume upon swelling is

considered, gel-type resins can be used without problem.35 An

alternative is the use of macroporous resins instead of micro-

porous gel-type polymers in order to prevent column blockage

due to polymer swelling, as they do not swell with solvents.16 The

third approach we have considered is the use of mini-flow

reactors based on monolithic materials. Monoliths are macro-

porous materials with a well defined structure of continuous

channels and confined spaces allowing a simple development of

flow-through reactor systems. They present high mechanical and

chemical stability and their morphological properties can be

finely tuned by adjusting the composition of the polymerization

mixture and reaction conditions. Functional groups can be

attached to the polymeric matrix either by grafting or by co-

polymerization,36 enabling very interesting applications as

supports for catalysts in continuous-flow processes.

The use of monolithic materials for reactor design has shown a

series of advantages compared with the use of bead gel-type

polymers, which have been highlighted by different authors.12–14

However, a clear experimental study has not been performed, so

far, to explain such differences.

Fig. 2 (a and b) illustrates the large differences in reactor

volume, for a column packed with the same amount of a gel-type

resin, in the presence of either a good swelling solvent (toluene)

or a non-swelling solvent (acetonitrile, ACN). In this case, an

adjustable device can be used to adjust the volume of the reactor

to that of the resin to prepare a reproducible flow through the

system. As shown in Fig. 2 the volume of macroporous resins, in

particular in the form of monoliths, is not affected by the

solvent. This figure also shows the profiles of the E(t) curves,

obtained for the toluene as the tracer, revealing the significant

differences in the corresponding flow patterns. When the gel-type

resin was not swollen, a very broad E(t) curve was obtained for a

flow rate of 1 mL min21. Under the same conditions, the

microporous resin swollen in toluene showed a more defined

pattern with a bimodal distribution, which may indicate the

presence of preferential channels, in good agreement with the

clear differences observed when the same packed gel-type

reagent, scavenger or catalyst is used with different solvents.1

On the contrary, as monolith polymers have a rigid structure, the

same E(t) curve is to be expected independent of the solvent

employed, as was experimentally seen (Fig. 2, right). For the

monolithic system, the flow pattern found was significantly

narrower than that obtained by reactors packed with gel-type

resins, implying a much more uniform and less dispersed flow

through the reaction vessel, thus being closer to an ideal plug

flow reactor. Hence, monolithic columns are expected to offer

better mixing and consequently offer superior yields and

selectivities in heterogeneous catalytic reaction systems, where

the contact between the substrates and the catalysts immobilized

on the surface of the support is critical. It is interesting to note

Fig. 2 Comparison of the flow patterns for mini-flow reactors packed

with different polymers at a flow rate of 0.5 mL min21. (a) Microporous

resin. (b) Monolithic column.

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that polymeric monoliths have been used not only as supports

for functional moieties but also as passive micromixers to

enhance mixing efficiency.37 This indicates that mini-flow

reactors based on monolithic materials offer clear advantages

over those based on gel-type resins.

The qualitative analysis of the E(t) curves can also be used as a

quality control to detect and understand the reactor defects or

anomalies. For instance, at low flow rates the mini-flow

monolithic reactor (Mfr-1) showed a long tail of tracer (Fig. 3,

left). This was indicative of the presence of some degree of back

mixing inside the reactor. In the case of the mini-flow reactor

Mfr-2, the E(t) suggested a possible channelling problem at low

flow rates (Fig. 3, right). This is probably due to the effect of

small channels between the polymer and the column wall that

served as preferential pathways for the fluid.

Noteably, the flow problems detected in both monolithic

columns were dependent not only on the inherent morphology of

the materials, but also on the flow conditions. In both columns,

an increase in the flow rate led to an increase of the symmetry of

the RTD curves, revealing the disappearance or minimization

of such disturbances (Fig. 4). This confirms the importance of

performing pulse tracer experiments as routine tests when

working with mini-flow reactors, since depending on the flow

conditions, misbehaving flow patterns might occur that could

affect their performance for the desired process. Moreover, these

experiments can be a useful control check during the lifetime of

the reactor to ensure that no blockade or channelling problems

are generated during long term use.

In order to compare the results, the E(h) curves corresponding

to different column packings at the same flow rate (1 mL min21

of ACN) have been represented in Fig. 5. They demonstrate how

the continuous porous structure of these monoliths is a very

suitable flow media, reflected in the narrow and high E(h) curves,

where the flow presents little axial dispersion and thus is closer to

plug flow than in the case of bead-type resin packings. As

expected, the packed reactor from smaller spheres (Mfr-3) shows

less dispersive flow than the non-ideal packing obtained from

larger beads (Mfr-4). Finally, the reactor from a microporous

Merrifield shows a very big dispersion of the tracer, indicating

that this type of polymer is much less appropriate for flow

applications

From the experimental E(t) curves, the mean residence time (t)

and s2 values were calculated. The results obtained are

represented in Table 3.

In all cases, t and s2 decreased with the flow rate. The values

of t for the different columns were very similar, indicating

comparable reactor volumes. However, important differences

were observed depending on the packing. The mini-flow reactor

based on the monolith with the lowest amount of porogenic

mixture (Mfr-1) showed a lower s2 in all the studied cases. This

means that the flow of the tracer through this packing was the

most homogeneous of all the studied cases, being the closest to

an ideal plug flow reactor. Since this packing had the lowest

porosity, the flow was also the most compact. On the other hand,

a monolith packing having a higher amount of porogenic

mixture lead to mini-flow reactors (Mfr-2) showing slightly

higher values of dispersion (higher values of s). Hence, the

higher porosity produced a higher dispersion of the fluid. The

packed reactors with a Merrifield macroporous resin (Mfr-3) or

with an Amberlite polymer (Mfr-4) showed higher values of s

due to the problems associated with the packing of the beads.

Fitting the results to the dispersion model

In any packed-bed reactor, a careful control is required to avoid

the formation of cracking or the floating of the beads as it may

lead to an inhibition of the flow and the contact of the substrates

and reagents with the active sites at the internal surfaces of the

resin. In this regard, the model selected to characterize the RTD

of the different packings was the axial dispersion. In this model,

the axial motion of a fluid is due to the bulk motion and to a

diffusive component characterized by a dispersion coefficient.38

Mathematically, this concept is described by the following:

Fig. 3 Flow disturbances observed at low flow rates in monolithic

columns. Left: The back mixing effect observed in the E(t) curve

corresponding to Mfr-1 at 0.5 mL min21. Right: The channelling effect

observed in the E(t) curve corresponding to Mfr-2 at 0.25 mL min21.

Fig. 4 E(h) curves corresponding to Mfr-1 (left) and to Mfr-2 (right)

using different flows of ACN as the solvent and toluene as the tracer.

Fig. 5 Comparison of E(h) curves for the different polymeric packed

columns obtained at a flow rate of 1 mL min21 of ACN, using toluene as

the tracer.

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LC

Lh~

Dax

uL

� �L2C

Lz2{

LC

Lz(6)

The parameter Dax characterizes the degree of back mixing

during the flow inside the reactor. The dimensionless group is

usually represented by the Peclet module.

Dax

uL

� �

~1

Pe(7)

Under ‘‘open’’ boundary conditions, i.e. the flow is undis-

turbed at the inlet and outlet of the vessel, eqn (6) has an

analytical solution:

E hð Þ~ 1

2

ffiffiffiffiffiffiPe

ph

r

e{Pe(1-h)2

4h (8)

The experimental results were adjusted to eqn (8) by numerical

integration, calculating the value of Pe that minimized the

average value of the sum of the squares:

e~

Ptmax

0

y tð Þ{ycalc tð Þ½ �

n

2

(9)

where n represents the total number of points measured. Eqn (9)

was minimized using a quasi-Newtonian method with quadratic

estimations and progressive derivatives. According to this

treatment, the experimental data were fitted to the axial

dispersion model. A very good agreement between the experi-

mental and calculated values was obtained in all the columns

studied (Fig. 6).

The Peclet values were higher for monolithic polymers than

for sphere packed columns (Fig. 7), indicating lower values of

Dax and thus a flow profile closer to a plug flow reactor.

A linear relationship was found between Dax and uL, which proved

that the model is consistent in the range of flow rates studied. Mrf-1

and Mrf-2 showed the lowest values of Dax. Thus, monolithic columns

are in all cases better systems for flow than sphere packed beds.

Monolithic polymers showed in all cases flow patterns closer

to an ideal plug flow than the bead-shaped packings. In the bead-

packing, a higher degree of back mixing was observed, resulting

in higher dispersion coefficients. An increase in the diameter of

the particles lead to a worse packing, which in turn was

characterized by a higher degree of mixed flow.

The different flow pattern of the substrates through each mini-

flow reactor studied has an important effect in continuous-flow

catalytic reactions, especially on those cases where fast reaction

kinetics might result in mass-transfer limited systems. This might

be the case for the Heck reaction between iodobenzene and

methyl acrylate at high temperatures in near critical ethanol.

Indeed, Table 4 shows that mini-flow reactors with lower values

of Dax present higher values of productivity. This is due to a

better flow distribution within the reactor, which results in lower

mass-transfer coefficients and better contact between the

substrates and the catalyst, which is on the inner surface of the

polymeric material. Other aspects that can influence the

productivity of each catalytic system are the morphology of

the Pd and the specific surface of the support. No significant

differences were found by SEM in the morphology of the Pd.

This was expected since the methodologies for deposition and

reduction were very similar. The specific surface of the support

was calculated for each reactor and even though a trend was

found, where higher values of productivity corresponded to

higher values of productivity, no direct correlation was observed.

Hence, even though the effect of the specific surface can not be

ruled out, the differences in productivity can be ascribed to the

flow patterns of each catalyst packing.

Conclusions

In this article, we have demonstrated that RTD tracer

experiments are very useful tools to characterize the flow patterns

within polymeric packed columns and as quality control tools to

Fig. 6 Fitting of the experimental results to the axial dispersion model for

Mfr-1. Solid lines: experimental results; dotted lines: calculated results.

(a) F = 1 mL min21. (b) F = 0.75 mL min21. (c) F = 0.5 mL min21. (d) F =

0.1 mL min21.

Table 3 Mean residence times and standard deviations for the differentreactors

Entry Mini-flow reactor F (mL min21) t (min) s2

1 Mfr-1 0.1 7.78 0.812 0.5 1.52 0.043 0.75 1.01 0.024 1 0.77 0.025 1.5 0.52 0.016 Mfr-2 0.25 4.11 0.227 0.5 2.06 0.078 0.75 1.38 0.049 1 1.04 0.0210 1.5 0.69 0.0211 Mfr-3 0.25 3.53 0.5312 1 0.89 0.0313 1.5 0.60 0.0214 2 0.46 0.0215 Mfr-4 0.5 1.48 0.5316 1 0.73 0.1517 1.5 0.48 0.0718 2 0.35 0.04

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detect defects or malfunctions in the columns. The different

mini-flow reactors have been modelled employing the axial

dispersion model. Monolith-based mini-flow reactors have proven

to be superior to bead-based packed reactors in terms of flow

distribution through the columns. This situation is reflected in lower

values of the corresponding axial dispersion coefficients. The

different flow patterns observed in the mini-flow reactors have

proven to be reflected in the productivity of Heck reactions catalyzed

by PdNPs supported on different kinds of polymeric systems, where

lower values of the axial dispersion coefficients correspond to higher

values of productivity. Thus, these tools can be used to easily

understand the different catalytic efficiencies found when comparing

different mini-flow reactors based on either monolithic or bead-type

polymers functionalised with catalytic sites.

Symbols

E(t) Residence time distribution curve (s)

C(t) Tracer concentration

t Mean residence time (s)

s Variance

h Dimensionless time

uL Mean liquid velocity (cm s21)

Pe Peclet module

Dax Dispersion coefficient (cm2 s21)

Acknowledgements

Work supported by CICYT (CTQ2008-04412/CTQ2011-28903),

Bancaja-UJI (P1-1B2009-58), and GV (ACOMP/2010/280).

References

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Fig. 7 Analysis of the results for the different polymeric packings employing the dispersion model. Left: Peclet values obtained as a function of the

linear velocity inside the reactors. Right: Axial dispersion coefficients calculated for each packing studied. Blue dots: Mrf-1; y = 0.081?x; R2 = 0.988.

Red diamonds: Mrf-2; y = 0.116?x; R2 = 0.996. Green triangles: Mrf-3; y = 0.402?x; R2 = 0.989. Black squares: Mrf-4; y = 0.557?x; R2 = 0.977.

Table 4 The correlation between the axial dispersion coefficients andthe productivity in a continuous-flow Heck reaction for different mini-flow reactorsa

Entry PdNPs-SILLPs uL (cm s21) Dax (102/cm s21) Productivityb

1 1 0.252 2.04 22.22 2 0.226 2.62 19.73 3 0.270 10.85 3.9a Reaction conditions: EtOH, 200 uC, 80 bar, 0.2 mL min21, 0.67 mol L21

of PhI in EtOH, 1 : 1.1 : 2 PhI : methylacrylate : Et3N molar ratio. b (molProduct)?x (mol cat)21?x min21.

This journal is � The Royal Society of Chemistry 2012 RSC Adv., 2012, 2, 8721–8728 | 8727

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8728 | RSC Adv., 2012, 2, 8721–8728 This journal is � The Royal Society of Chemistry 2012

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