Advances and problems of frontal polymerization processes

ISSN 2079�9780, Review Journal of Chemistry, 2011, Vol. 1, No. 1, pp. 56–92. © Pleiades Publishing, Ltd., 2011.Original Russian Text © S.P. Davtyan, A.A. Berlin, A.O. Tonoyan, 2011, published in Obzornyi Zhurnal po Khimii, 2011, Vol. 1, No. 1, pp. 58–96.

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CONTENTS1. Introduction.2. Frontal polymerization of acetaldehyde and methylmethacrylate under extreme conditions.2.1. Polymerization of acetaldehyde under cryogenic temperatures.2.2. Radical frontal polymerization of methylmethacrylate under high pressures.3. On critical transitions of the thermal modes of radical polymerization: Regulation of the yield and molec�

ular�weight characteristics of polymer.4. Radical frontal polymerization under atmospheric pressure.5. Effect of initiating systems on the frontal modes of radical polymerization.5.1. Effect of the nature of the initiator, monomer, and disperse inorganic additives on the reaction order with

respect to the initiator.6. Temperature profiles of frontal polymerization.7. Advances in frontal polymerization.7.1. Thermochromic composites.7.2. Polymer nanocomposites.7.3. Synthesis of intercalated superconductive polymer�ceramic nanocomposites.7.4. Interpenetrating polymer nets.7.5. Functionally gradient materials.7.6. Polymerization in laminar flows.7.7. Polymerization in turbulent flows.8. Problems of frontal polymerization.8.1 Frontal solidification of resorcinol diglycidyl ether by 4,4�diaminodiphenyl sulfide.8.2. Frontal polymerization of ε�caprolactam.9. Conclusions.

Advances and Problems of Frontal Polymerization ProcessesS. P. Davtyana, A. A. Berlinb, and A. O. Tonoyana

a State Engineering University of Armenia, ul. Teryana 105, Yerevan, 0009 Armeniab Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina 4, Moscow, 119991 Russia

Received June 28, 2010; in final form, July 21, 2010

Abstract—The main stages of the development of frontal polymerization are presented. The processes takingplace at cryogenic temperatures, under high (up to 5 kbar) pressures and usual conditions, when the polymer�ization is performed in glass ampoules without excessive pressure, are discussed. Depending on the Semenovparameter, the conditions of polymerization in low�temperature quasi�isothermal and high�temperature adi�abatic or frontal thermal modes are considered. Theoretical and experimental data for the dependence of thefront velocity on the nature of the initiator, monomer, and nano� and microadditives and their quantities onthe reaction order with respect to the initiator are analyzed. Monomers polymerizing in the reaction frontpropagation are classified regarding their polymerization rates and boiling temperatures. The articles of var�ious authors devoted to the synthesis of polymer materials and polymer�based composites difficult to obtainunder conventional conditions are considered. The reactors of frontal polymerization in turbulent and lam�inar flows, widely applied in practice, are studied. Certain conclusions are made on the further developmentof frontal polymerization processes on the basis of data available in the literature.

Keywords: frontal polymerization, cryogenic temperature, high pressure, molecular weight, polydispersity,convective mass�transfer, temperature profile, thermochromic composites, polymer nanocomposites, rela�tive heat capacity, rigid amorphous fraction, glass�transition temperature, interpenetrating polymer net�works, functionally gradient materials, reactor with radial symmetric laminar flows, turbulent flow reactor

DOI: 10.1134/S207997801101002X

REVIEW JOURNAL OF CHEMISTRY Vol. 1 No. 1 2011

ADVANCES AND PROBLEMS OF FRONTAL POLYMERIZATION PROCESSES 57

1. INTRODUCTION

Frontal polymerization is a nonisothermal process propagating by an autowave mechanism. The first workson frontal polymerization were performed at the Institute of Physical Chemistry and the Branch of the Instituteof Chemical Physics of the Soviet Union Academy of Sciences in the 1970s. Since the process is nonisothermal,the fundamental kinetic and macrokinetic regularities and peculiarities were studied by the example of the poly�merization of different monomers under adiabatic conditions. It was found that the nonisothermicity of the pro�cess changed rather significantly the main postulates of kinetics and thermodynamics with respect to isothermalprocesses. Using the example of adiabatic polymerization, the effect of different inducing methods (mixture oftwo initiators, successive substantial and thermal inducing procedures, etc.) and the gel effect on the conversionrate and the molecular�weight characteristics of a polymer were theoretically and experimentally investigated;the limits of applicability of the principle of quasi�stationary concentrations were determined. These regularitieswere specified for the case of frontal polymerization, and the kinetic and macrokinetic regularities of the pro�cesses occurring in the frontal mode were conclusively established.

Note that, until the 1990s, frontal polymerization was investigated solely by Russian chemists from the Insti�tute of Chemical Physics and the Branch of the Institute of Chemical Physics of the Soviet Union Academy ofSciences, where a powerful research center on frontal polymerization was established. On the basis of accumu�lated experience, scientific fundamentals were developed for the technological implementation of continuousfrontal polymerization.

It should be noted that the most advantageous factor of frontal polymerization, from the implementationpoint of view, is that the process can be performed in continuous reactors in laminar and, particularly, turbulentflows.

After 1991, Prof. J. Pojman (Mississippi State University, United States) joined the research. (The first for�eign work was published by J. Pojman in 1991.) Due to his efforts, frontal polymerization is currently of researchinterest in many countries. It is worth noting that, in spite of the valuable contribution scientists from differentcountries have made to the study of frontal polymerization, the technological processes developed in the Russianresearch group—different tubular reactors with turbulent flows and a cylindrical reactor with radial symmetricflows—are only implemented for commercial practical use.

It is regrettable that in many contemporary publications concerning frontal polymerization, not only are theoriginal works performed both before and after the 1990s not cited, but the history of the development of frontalpolymerization is given incorrectly, with an inaccurate chronology. We therefore consider it necessary, along withthe advances and problems of frontal polymerization, to present briefly the development of the issue highlightedby the analysis of pioneering works; to consider different authors’ experimental data, which cannot be explainedby the contemporary concepts of frontal or radical polymerization; and, finally, to summarize the advances andproblems in this promising field.

2. FRONTAL POLYMERIZATION OF ACETALDEHYDE AND METHYLMETHACRYLATE UNDER EXTREME CONDITIONS

2.1 Polymerization of Acetaldehyde under Cryogenic Temperatures

The history of frontal polymerization began during the investigation of the polymerization of acetaldehydeunder cryogenic temperatures. It should be noted that the autowave propagation of polymerization was viewedby the authors of [1] as a result of not only thermal but also physical effects (the front was revealed also in thebreaking off of the tip of a frozen sample). Because the main goal of the work was the study of the solid�phasepolymerization of acetaldehyde under the effect of γ�radiation, and the yield of the polymer under these condi�tions was insignificant, the phenomenon of the frontal propagation of a polymerization thermal wave did notbecome a key issue in the studies. The polymerization of acetaldehyde in the frontal mode was observed after thecooling of the initial reaction mixture to ~183 K, the γ�radiation treatment using a Co�60 source, and the heatingof the upper part of the ampoule. As a result, the formation of the thermal waves of the solid�phase polymeriza�tion of acetaldehyde was observed, propagating vertically downward. The typical temperature profiles for thesolid�phase frontal polymerization of acetaldehyde obtained in glass ampoules 2.2 mm in inner diameter and100 mm in length [1] are presented in Fig. 1.

Two interesting facts can beseen in curves 1–3 (Fig. 1): (1) There is immediate heating in the reaction zone(there are large temperature gradients), and (2) the largest heating value in the reaction zone is only ~20 K,regardless of the position of the thermocouples. Analysis of the results presented in [1] shows that an immediateincrease in the front temperature is observed. In addition, the largest heating values of thermal polymerizationwaves are only ~10–35 K, independently of radiation dose (0.5–10 Mrad; i.e., the initial radical concentrationis (0.5–10) × 10–3 mol/l, respectively), inner diameters of reaction ampoules (1.6–5 mm), and ambient temper�ature (148–258 K). Here, the front velocity changes from 43 to 162 cm min–1 depending on the radiation dose;

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DAVTYAN et al.

the dependence of the front velocity (u) on the radiation dose (γ) is described by a power law; that is, u ~ γn,where the value of n, according to the data of [1], is ~0.3. Comparison of the limiting heating values with theresults obtained in [2] allows the determination of the conversion rates, which are ~(0.1–0.35), respectively.Small heating values and low conversion rates were associated with the closing of the growing active sites on thedefects of monocrystalline acetaldehyde, followed by their termination [1]. However, the solid�phase frontalpolymerization of acetaldehyde occurs by a radical mechanism, according to the data presented. Therefore, itmay be suggested that the observed low conversion rates can be the result of either the bimolecular terminationof macroradicals or the termination of macroradicals by unfrozen low�molecular radicals or other particles.

It is obvious that the above results are difficult to explain within the general theory of frontal polymerization.Indeed, regardless of the polymerization mechanism (ionic [13], radical [4–10], polycondensation of epoxycompounds [11–14], and others), the front velocity changes from ~0.5 to 6 cm min–1, which is more than anorder of magnitude lower than the front propagation velocity of the polymerization of solid�phase acetaldehyde.

The abnormally high propagation velocities of the solid�phase frontal polymerization of acetaldehyde can becaused by both entropy or energetic factors and their combined effect.

The entropy factor can be the result of the advantageous relative position of the monomer molecules in thecrystalline grid of the acetaldehyde monocrystal. In this case, the reaction of chain propagation can occur almostwithout steric hindrances. As a result, a rather significant increase in the polymerization rate can occur becauseof the pre�exponential factor of the rate constant of chain propagation. On the other hand, the presence of hightemperature gradients in the reaction zone, in its turn, can cause a mechanical chemical activation (formationof microcracks in front of the reaction zone [15]) of the process of solid�phase polymerization and, thereby, con�siderably reduce the activation energy of polymerization. Both individual and combined effects of said factorscan cause abnormally high values of the front velocity of the solid�phase polymerization of acetaldehyde. It isnecessary to note that the investigation of the solid�phase frontal polymerization of aldehydes and, particularly,acetaldehyde can be of practical interest, if ways are found to increase the yield of the resulting polymer. Theintroduction of peroxide initiators to the initial reaction mixture can probably solve the problem. In this case,the initial formation of frontal modes under the effect of γ�radiation and the presence of high temperature gra�dients can be an inducing mechanism of the low�temperature decomposition of initiators. Therefore, one canexpect that the formation of the stationary frontal modes of solid�phase frontal polymerization with the partic�ipation of formed free radicals can lead to a considerable increase in the conversion rate.

On the other hand, the solid�phase frontal polymerization of aldehydes only under the effect of γ�radiationis useful for determining the elementary rate constants of the occurring reactions.

The solution of the abovementioned problems obviously requires serious experimental and theoretical inves�tigations of the solid�phase frontal polymerization of aldehydes, both under conditions of solo γ�radiation andwith the addition of peroxide initiators.

It should be particularly noted that incomplete conversion of a monomer into a polymer is characteristic forthe high�temperature thermal modes (adiabatic and frontal) of the radical polymerization of vinyl monomers,as well. Therefore, it is of practical interest to consider if the yield and molecular�weight characteristics of thepolymer formed under the noted thermal modes can be governed. This issue is briefly discussed below.

120

1

140

23

T, K

Time

Fig. 1. Temperature profiles of the solid�phase frontal polymerization of acetaldehyde [1].



2.2. Radical Frontal Polymerization of Methylmethacrylate under High Pressures

In the high�temperature thermal modes of radical polymerization, a considerable increase in the conversionrate can be attained by performing polymerization under high pressures. Indeed, high pressures (1000–5000 atmor more) affect in different ways the elementary reactions of chain initiation, propagation, and termination.

The rate constants of the reactions depend on pressure as follows:

, (1)

where is the difference between the volumes of interacting molecules involved in the activated complex andin the initial state.

In the case of a monomolecular reaction of decomposition of an initiator, the formation of the activated com�

plex is accompanied by some stretching of the destructing bonds. Therefore, for this reaction is a positivevalue, and an increase in pressure leads to a decrease in the initiation rate. For conventional initiators, the value

of is ~(5–10) cm3 mol–1 [16, 17]; therefore, an increase in pressure from 1 to 3000–5000 atm leads to adecrease in the rate constant of the decomposition of the initiators by more than 3–5 times.

The value of for the rate constants of the bimolecular reactions of chain propagation and termination isnegative and accompanied by a decrease in volume in the transition from the initial state to the activated com�

plex. For vinyl monomers (styrene, methylmethacrylate, and others), the value for the chain�propagationreaction varies within the range of approximately –13 to –20 cm3 mol–1. Therefore, with the increase in pressureto 5000 atm, the rate constant increases by more than an order of magnitude.

The dependence of the rate constant of the bimolecular termination of chains on pressure is not governed byEq. (1), because the reaction medium becomes more viscous, the gel effect appears, and the value of the rateconstant rapidly decreases. It is obvious that the decrease in the rate of decomposition of the initiator and thebimolecular chain termination processes, along with the increase in the polymerization rate, considerablyincreases the conversion rate. The decrease in the rate of decomposition of the initiator leads to an increase inthe lifetime of the growing chains, which, in turn, is a positive factor regulating the conversion rate and themolecular�weight characteristics of the polymer.

It is considered in [18] that high pressures were used [4, 5] to prevent both boiling of the monomer and grav�itational convective mass transfer [19, 20] in the propagation of the thermal polymerization waves of methyl�methacrylate vertically downward. It is known, however, that the convective mass transfer of the polymer fromthe reaction zone into the monomer solution by gravitation can be avoided by increasing the viscosity of the ini�tial reaction mixture, for example, by dissolving 10–12% of its own polymer, whereas the boiling of methyl�methacrylate is completely terminated even at pressure values of 5–6 atm. Therefore, the statement that highpressures were used in the frontal polymerization of methylmethacrylate to prevent the boiling of the monomerand gravitational convective mass transfer [18] is not consistent.

The investigation of the frontal polymerization of methylmethacrylate and 3�(oxyethylene)�γ,ω�dimethacrylate under the effect of different initiators (benzoyl peroxide, dicyclohexyl peroxydicarbonate) athigh pressure showed that the polymerization wave front was flat [4, 5, 21, 22]. The structure of temperature pro�files and the effect of the nature and concentration of the initiator, pressure, and initial temperature on the frontpropagation velocity were studied [4, 5, 21, 22].

The analytical equation for the front velocity and the conversion rate was obtained with the use of the approx�imation of narrow reaction zones [23–25]. Comparison of the theoretical [23–25] and experimental [4, 5, 21,22] values of the stationary front velocity and the conversion rate (αtr) shows that they disagree significantly witheach other. According to the experimental data, the monomer almost completely transforms into the polymer,while in theory the conversion rate is only ~0.5–0.6. Such disagreement between the theoretical and experimen�tal data is explained by the effect of high pressures on the elementary rate constants of the polymerization reac�tion and by a rather strong gel effect [25]. Indeed, consideration of the influence of pressure and the gel effecton the kinetic constants and on the dependence of the thermal conductivity coefficient on pressure enabled thecomplete quantitative description of the experimental results.

3. ON CRITICAL TRANSITIONS OF THE THERMAL MODES OF RADICAL POLYMERIZATION: REGULATION OF THE YIELD AND MOLECULAR�WEIGHT CHARACTERISTICS

OF A POLYMER

The thermal mode of the polymerization process is determined by a balance between heat elimination in thereaction and heat transfer to the environment through the walls of the reaction vessel. If the heat removal is moreintensive than the heat elimination rate, as a rule, an isothermal reaction mode is usually implemented. Other�wise, the reaction mixture is heated and transferred into a high�temperature mode. Following the materials pub�

г#lnd K dp V R T= −Δ

#VΔ

#VΔ

#VΔ

#VΔ

#VΔ

60


DAVTYAN et al.

lished in [26, 27], let us discuss the conditions for the formation of high�temperature modes of the radical poly�merization of vinyl monomers and the possibility of regulating the yield, molecular weights, and width of themolecular�weight distribution. Consider the conventional mechanism (decomposition of an initiator, propaga�tion and bimolecular termination of chains) of radical polymerization in a batch reactor with heat dissipation tothe environment according to Newton’s law.

The process of radical polymerization is described by an equation system considering the reactions (decom�position of an initiator, consumption of a monomer, bimolecular termination of chains) and the thermal bal�ance, with the addition of five moment equations for the molecular�weight distributions (MWD) for growing andterminated macroradicals.

The numerical solution enabled the obtaining of the changes in time not only at all concentrations and tem�peratures, but also in the moments of MWD and, consecutively, number�average ( ) and weight�average ( )

molecular weights and polydispersity for the entire polymer [27]

(2)

where , , and were the zeroth, first, and second moments of MWD for theentire polymer. Here, the main attention was paid to the changes in temperature, conversion rate, and molecu�lar�weight characteristics in dependence on the value of heat removal to the environment. The results of thesolution were examined using the Semenov parameter, known in the combustion theory of thermal explosion[26]; that is,

, (3)

which characterizes the ratio of the heat elimination rate and the heat removal rate.The results of the numerical solution were analyzed for the parameter values typical for the radical polymer�

ization of vinyl monomers and, particularly, for the polymerization of styrene and methylmethacrylate [28, 29].It is known from the theory of thermal explosion [26] that there is a critical value of the parameter (Secrit).

According to the Semenov parameter, when Se < Secrit, the heating value of the system is small (no more than15–20°) and the reaction occurs in a low�temperature mode that is close to isothermal conditions, while at Se >Secrit the process is developed with a significant heating, i.e., in a high�temperature explosion mode. On thisbasis, consider the effect of the value of Se on the limiting heating temperature (Tlim), conversion rate (αlim),

weight�average molecular weight , and polydispersity of the polymer . The mentioned depen�dences for the radical polymerization of styrene are presented in Fig. 2. In the curve (Fig. 2a), a clear stepwisechange is observed in the limiting heating temperature corresponding to the transition from the low�temperature(quasi�isothermal) mode to the high�temperature (quasi�adiabatic) mode. Such a stepwise change in the valueTlim is characteristic for the polymerization of both styrene and other vinyl monomers. Therefore, on the basisof the data presented in Fig. 2, it can be argued that, for the processes of radical polymerization of vinyl mono�mers, there is a critical value of the Semenov parameter (Secrit) leading to a sharp change in the thermal poly�merization modes. Therefore, for the radical polymerization of vinyl monomers, there are two thermal modesseparated by the critical value of parameter Se. It also follows from Fig. 2 that the stepwise change is observednot only for the limiting heating temperature but also for values αlim (Fig. 2b), (Fig. 2c), and (Fig. 2d).

The stepwise decrease in the limiting conversion rate in the transition from low�temperature to high�temper�ature mode is caused by the exhaustion of the initiator [27] due to a sharp increase in temperature, which isrelated to a higher activation energy of the reaction of decomposition of the initiator. The exhaustion of the ini�tiator, in turn, leads to a sharp increase in the concentration of primary radicals and to a further increase in the

rate of bimolecular termination ( ) with respect to the rate of chain propagation ( ). As aresult, a decrease in the limiting conversion rate (Fig. 2b) and in weight�average molecular weight (Fig. 2c) anda stepwise increase in polydispersity of the resulting polymer (Fig. 2d) are observed. To determine the reasons fora sharp change in molecular�weight characteristics (Fig. 2d), it is necessary to compare the kinetic curves of theconversion rate and consumption of the initiator. These data are presented in Fig. 3.

It follows from Fig. 3 that, after the initiator is almost completely decomposed (curve 1), monomer con�sumption in the post�polymerization section is observed to be ~2–3%. Here, with the decrease in the concen�tration of growing macroradicals, the lifetime of macroradicals increases because of the bimolecular terminationof chains. Therefore, in this part of the polymerization process, a super�high�molecular fraction of macromol�

nP wP

w nP P

( )

( )

( )

( )

2

; ,j j j j

n w

j j j j

j R P j R PP P

R P j R P

+ +

= =

+ +

∑ ∑∑ ∑

( )j jR P+∑ ( )j jj R P+∑ ( )2j jj R P+∑

eff

g /0 0 0 0 0

20

( ) ( ) ( )p i tQM k T I k T k TESe

hS VR T=

( ) limwP ( ) limw nP P

( ) limnP ( ) limw nP P

( )2

t jK R∑ ( )p jK R M∑



ecules is formed, and the entire polymer has a higher weight�average molecular weight than the polymerobtained before the decomposition of the initiator.

It is interesting that in the post�polymerization section, the number�average polymerization rate

remains almost constant. This is because, after the exhaustion of the initiator, the number of

polymer macromolecules remains the same; that is, = const, while the first moment of MWD

increases insignificantly (MK is the residual concentration of the monomer) [27]. The

formation of the superhigh�molecular fraction of polymer chains affects the second moment of MWD ( )much more strongly; therefore, the weight�average molecular weight is much more sensitive to the superhigh�molecular “tail” formed at the very final stages of polymerization. Consequently, the formation of such a high�molecular fraction after the complete decomposition of the initiator is the main reason for the sharp broadeningof MWD for the polymer obtained by the radical polymerization of vinyl monomers in high�temperature modes.

It is apparent that, for any high�temperature modes of radical polymerization (adiabatic or frontal), theexhaustion of the initiator has a similar effect on the limiting conversion rate and the MWD characteristics ofthe resulting polymer. Therefore, the approaches developed for regulating the yield and the MWD characteristics

( )

( )j j

nj j

j R PP

R P

+

=

+

∑∑

( )j jR P+∑( ) 0j j Kj R P M M+ = −∑

2jj P∑

0.4

4

0

8

0.8 1.2

(c)

Pn × 10–2–

Se 0.4

3.0

0

3.5

0.8 1.2

(d)

Pw/Pn–

Se

350

400

(а)

Tlim, К

0.50

1.00

(b)

αlim, К

–

4.0

2.5

2.0

0.25

0.75

0

450

300

Fig. 2. Change in the limiting values of (a) temperature, (b) conversion rate, (c) number�average molecular weight, and (d) poly�dispersity [27].

62


DAVTYAN et al.

of the polymer in the processes of radical polymerization in an adiabatic mode [27] can be successfully appliedfor frontal polymerization.

Let us briefly consider the developed approaches [27] that enable the regulation of the conversion rate andthe MWD characteristics of the polymer formed in any high�temperature modes.

The study of the effect of different initiation methods (one initiator, a mixture of two initiators, complicatedinitiation (initiator + thermal initiation)) on the kinetics and the yield of the resulting polymer showed that,under conditions of adiabatic polymerization of vinyl monomers, a considerable increase in the yield wasattained at the initiation by a mixture of two initiators differing in activation energies of the rate constants of thedecomposition reaction [27]. In the successive initiated and thermal polymerization, the yield of the polymercorresponded to almost complete conversion of the monomer into the polymer.

The results of the experimental study of the kinetics of the radical polymerization of styrene, methyl�methacrylate, and n�butylmethacrylate under the effect of different initiators (dicyclohexyl peroxydicarbonate(DCPC), benzoyl peroxides (BP), tert�butyl peroxides (TBP), azoisobutyric acid dinitrile (AIBN), and their

30

0.2

0 15 6045 9075

0.1

0.4

0.3

0.5

0.4

0.2

0.8

0.6

1.01

2

α I/I0

Time, min

Fig. 3. Kinetic curves of the change in (2) the conversion rate and (1) the consumption of the relative concentration of the initi�ator.

10

100

050

20 30 40

150

200

250

T, °C

1

2

Time, min

Fig. 4. Kinetic curves of the increase in reaction temperature during the adiabatic polymerization of (1) methylmethacrylate inthe presence of 15% of the initial monomer and (2) n�butylmethacrylate in the initiation by a mixture of BP and TBP [27].



mixtures) [27] showed quantitative agreement with the results of theoretical investigations. It was shown, in par�ticular, that the enhancement of the gel effect at the beginning of the polymerization of methylmethacrylate orn�butylmethacrylate (dissolution of its own polymer in the initial reaction mixture, decrease in the initial tem�perature of polymerization, etc.) can cause an almost complete exhaustion of the monomer (Fig. 4).

It is obvious that under conditions of radical polymerization in the high�temperature modes, the role of ther�mal initiation increases because of the continuous increase in temperature. Therefore, at certain temperatures,thermal initiation can become a main source of primary radicals of polymerization after the exhaustion of theinitiator.

Indeed, the adiabatic polymerization of n�butylmethacrylate caused by TBP is characterized by a two�stepincrease in the reaction temperature (Fig. 4, curve 2), where the second step is related to thermal polymeriza�tion.

It is necessary to add that, in any high�temperature polymerization mode, an increase in the polymer yieldleads to an increase in molecular weights and a decrease in polydispersity of the resulting polymer. For example,a decrease in polydispersity in the polymerization by a mixture of two initiators is associated with a decrease inthe polymerization rate because of a considerable decrease in the concentration of the residual monomer afterthe exhaustion of the second, “high�temperature,” initiator. Namely, these approaches were successfully appliedfor regulating the conversion rate and the MWD characteristics in the radical frontal polymerization of vinylmonomers [11, 30–35].

4. RADICAL FRONTAL POLYMERIZATION UNDER ATMOSPHERIC PRESSURE

In frontal polymerization under conventional conditions (atmospheric pressure, initial temperature of thereaction mixture ~25–100°С), the presence of gravitational convective mass transfer (the Taylor instability) ornatural convection can cause the degeneration of frontal modes for many monomers. The intensity of the men�tioned processes is determined by a number of factors, such as the functionality of the monomers and the aggre�gate state (liquid, crystalline) of not only the monomers but also the resulting materials (viscous�flow, crystalline,glassy, cross�linked, etc.). On the basis of these considerations, Pojman et al. [36] divided the correspondingmonomers into three groups to study polymerization in the stable frontal modes. However, given the fact that thepolymerization rate plays an important role in the formation of stable frontal modes, it is more suitable to qualifythe monomers for frontal polymerization by five points.

As in [36], multifunctional monomers polymerizing by a free�radical mechanism [37–43] and epoxy com�pounds [11–14, 44, 45] that undergo polycondensation under the effect of aromatic and aliphatic amines can bebrought into the first group. Acrylamide, its derivatives, and other monomers whose radical polymerization andcopolymerization in aqueous solutions yield the formation of hydrogels can also be placed in the first group [40–43]. For these systems, the formation of densely or rarely cross�linked steric network structures prevents gravi�tational convective mass transfer; therefore, the frontal modes propagating vertically downward are not degen�erated. However, for the upward frontal modes, when the front is initiated by temperatures significantly exceed�ing the temperature of adiabatic heating, a natural convection of low�boiling components of the initial reactionmixture can be observed [12].

The second group, as in [36], can consist of monomers in which their own polymers are insoluble and, beingin a viscous�flow state, have high shear viscosity. High shear viscosity and adhesion to the reactor walls create theconditions for the formation of stable frontal modes for these monomers [44], for both downward and upwardthermal polymerization waves.

Most likely, powder crystalline monomers (acrylamide, acrylamide complexes with nitrates of transition met�als, vinylpyrazols and their derivatives, and others) should be placed in the third group. For monomers of thistype, the formation of the frontal modes depends on the thermal effect of polymerization and the melting pointof the crystalline monomers. The powder crystalline monomers with melting points of ~(70–90)°С (acrylamide[46, 47] and Co�, Ni�, and Mn�containing metal�complex monomers [8–10, 48]) lead to the formation andpropagation of the stable frontal modes of radical polymerization of the initial reaction mixture even at roomtemperature. In the case of crystalline monomers with thermal effects close to that of the polymerization of acry�lamide but having melting points of more than 170–180°С (vinylpirazols and their derivatives, etc.), the frontalmodes are not formed with the reaction mixture at room temperature, even if a hot surface (~300°С) is appliedto the side face of the reaction ampoules. In the layers closest to the side face, only the melting of the crystallinemonomer is observed without further polymerization. In order to polymerize these monomers in the mode ofthe propagation of thermal waves, either partial dissolution of the monomer in the corresponding solvents or theincrease of the initial temperature of the reaction mixture to ~170°С is necessary.

The fourth group is represented by monomers with low boiling points, e.g., isobutylene (Тbp = 6.9°С), iso�prene (Тbp = 34°C), and others. These monomers are characterized by a superhigh polymerization rate and, as

64


DAVTYAN et al.

a rule, can form the frontal modes [49–63]. The processes occurring with a high rate, for example, the obtainingof chlorobutyl rubbers [50–52, 64–67], can also be assigned to the fourth group. High rates of the polymeriza�tion process, as a rule, lead to high rates of the reaction front propagation; therefore, gravitational mass transferdoes not occur.

The fifth group includes a wide range of monomers whose boiling points are lower than their temperatures ofadiabatic heating and whose polymers are soluble in their own monomers. In the opinion of the authors of [36],two adverse factors can lead to the degeneration of frontal modes for many monomers of this type: the Taylorinstability and the boiling of monomers in the process of frontal polymerization.

To prevent gravitational convective mass transfer, it was proposed to rotate the reactor around the axis of frontpropagation at a rate of 1300 rpm [68], which is technologically difficult for real processes. Therefore, methodsfor stabilizing the frontal modes for monomers of the fifth group should be discussed more thoroughly.

The gravitational convective mass transfer of a viscous�flow polymer begins with the high�molecular fractionof the polymer leaving the reaction zone because of its higher local density, and continues with the settlement ofthis part of the polymer from the reaction zone into the monomer solution [20]. The necessary condition forgravitational convective mass transfer is a higher velocity of downward settlement (Vgr) of the dense polymer withrespect to the front velocity (Vfr); that is, Vgr > Vfr. Otherwise, if Vgr ≤ Vfr, gravitational convective mass transferis obviously not observed. The conditions Vgr > Vfr and Vgr ≤ Vfr are determined not only by the gradient of den�sities of the melted polymer (situated in the reaction zone) and the monomer (situated directly below the reac�tion zone) but also by the viscosity of the unreacted reaction mixture, that is, the initial monomer with the ini�tiator. Therefore, in frontal polymerization, the intensity of gravitational convective mass transfer can be regu�lated by the viscosity of the initial reaction mixture by dissolving the polymer in its own monomer. Indeed, thedissolution of ~10% of polymethylmethacrylate completely eliminated the Taylor instability in the frontal poly�merization of methylmethacrylate [20]. Obviously, the amount of polymer necessary for dissolution in its ownor a foreign monomer is determined by the nature of the monomer and depends on the initial temperature of thereaction mixture. The viscosity of the initial reaction mixture was increased by adding silicates to avoid the Taylorinstability [69].

It should also be noted that the polymer additives to the initial reaction mixture lead to an increase in thepolymer yield because of both the decrease in the limiting temperature of frontal heating and the enhancementof the gel effect at the initial stages of frontal polymerization. As mentioned above, the addition of small amountsof polymer in combination with moderate pressures (5–6 atm) can significantly increase the boiling point of themonomer, which is also a positive factor for the formation of stationary frontal modes.

For some monomers of the fifth group, the selection of the initial temperature of the reaction mixture can beessential for the formation of stable frontal modes. The point is that the variation of the initial temperatureenables the change in the limiting heating temperature of thermal waves, so that it appears to be less than thetemperature of glass transition or crystallization of the corresponding polymers. The formation of a solid poly�mer in the process of frontal polymerization is a positive factor from the gravitational convective mass transferpoint of view.

Therefore, analysis of articles [8–10, 37–69] shows that the conditions can be selected for many monomersto be polymerized at the stationary propagation of the reaction front.

It is obvious that the nature and concentration of initiating systems can also affect the stability and other mac�rokinetic characteristics of the frontal polymerization modes.

5. EFFECT OF INITIATING SYSTEMS ON THE FRONTAL MODESOF RADICAL POLYMERIZATION

It is known that the thermal decomposition of many initiating systems is accompanied by the elimination ofCO2, NO2, and other gases.

According to the data of [36], the decomposition of peroxide initiators in the reaction zone and, consecu�tively, pore formation due to the elimination of CO2, NO2, and other gases in the polymer volume, along withother gaseous inclusions, can increase the front velocity by 25–30%. It should be noted that the radial migrationof gaseous inclusions from the periphery to the center (just in front of the reaction zone) transforms the convexshape to the flat plane shape of the front. The investigation of frontal polymerization under the effect of pressure(up to 30 tm) showed that the front velocity depends linearly on the reciprocal value of the pressure [36]. Suchdependence can be related to the suppression of gas formation under the effect of moderate pressures.

It is obvious that if initiators are the only sources for the formation of gas inclusions (pores), the use of potas�sium, sodium, or other persulfates in frontal polymerization processes does not lead to pore formation. For thispurpose, special initiators were synthesized for frontal polymerization processes [70]. However, considering thatporous materials with either open or closed pores have been widely used in different technical fields for a long



time [71, 72], the application of gas�containing initiators under conditions of frontal polymerization can be ofparticular interest. Gas�containing initiators become especially important for obtaining polymer materials withnanoscale pores in the processes of frontal polymerization. In this case, the use of moderate pressures and theselection of the conditions of frontal polymerization enable the regulation of both the pore size and the uniformdistribution of pores in the matrix of a polymer nanocomposite.

It is necessary to add that, aside from the nature of the monomer and initiator, the selection of the conditionsof frontal polymerization and the thermal mode of further cooling of the polymer samples to the temperature oftheir operation are technologically very important. Therefore, these issues are discussed in a separate section.

The nature and concentration of initiators, as already noted, affect both the stability of frontal modes and thefront velocity. The order of the dependence of the front velocity on the concentration of the initiator dependsrather considerably both on the nature of the initiator and monomer and on the aggregate state of the latter.These questions are also considered more thoroughly.

5.1. Effect of the Nature of the Initiator, Monomer, and Disperse Inorganic Additiveson Reaction Order with Respect to the Initiator

It is known from the theory of frontal polymerization that, for the three�stage radical polymerization of vinylmonomers, the front velocity depends on the initial concentration of initiators by a power law; that is,

[6, 23–25]. Here, u is the front velocity; I0 is the initial concentration of the ini�tiator; n is the reaction order with respect to the initiator; and function f(xi) depends on the concentration of themonomer, the pre�exponential factor, the activation energy of the effective rate constant of polymerization, thethermal conductivity coefficient, the thermal effect of polymerization, the gel effect, the final conversion rate,the temperature of adiabatic heating, and other parameters [23, 35].

It is interesting that, by the results of numerical calculation, the value of n was found to be 0.40 [6], while bythe results of analytical solution it was 0.48 [23, 24]. However, it was shown in early articles [21, 22] that in thefrontal polymerization of 2�(oxyethylene)�γ,ω�dimethacrylate (OEDMA) and methylmethacrylate under highpressures (up to 5 kbar), the value of n depends on the nature of the initiator and monomer. For example, in thefrontal polymerization of OEDMA under the effect of peroxide initiators such as di�tert�butyl peroxide (TBP),benzoyl peroxide (BP), and dicyclohexyl peroxydicarbonate (DCPC), the values of n were 0.22, 0.32, and 0.34,respectively; for methylmethacrylate (initiator BP) it was 0.36.

On the basis of these results alone, it may be supposed that these variations of the value n are due to the spe�cific effect of high pressures on the efficiency of initiation, chain termination, etc. However, upon further inves�tigation of the frontal polymerization of methacrylic acid and triethyleneglycol dimethacrylate (TEGDMA)under normal conditions, the following n values were found for azoisobutyric acid dinitrile (AIBN), cumyl per�oxide (CP), lauryl peroxide (LP), and TBP: 0.24, 0.25, 0.27, and 0.26, respectively; for AIBN, BP, and LP thevalues were 0.2, 0.23, and 0.31, respectively. The data on the effect of the nature and concentration of the initi�ator on the value of n for the radical frontal polymerization of acrylamide are also interesting to consider. Theeffect of the concentration of BP and AIBN on the frontal polymerization rate of acrylamide, obtained in [46],is illustrated in Figs. 5a and 5b. As seen from Fig. 5, at a package density of the initial reaction mixture of 0.95–1.0 g cm–3, the obtained dependence is almost the same for the downward (curve 1) and upward (curve 2) waves,

and it is described by the equation .

( ) ( )[ ]1/2 1/21/2

0 0n

i iu I f x I f x⎡ ⎤= =⎣ ⎦

0.43 0.020~u I ±

0.2

4

0

(а)

2

6

u, c

m m

in–

1

0.4 0.6 0.8

1

2

wt %0.5

(b)

1.0 1.5 2.0

1

2

0

Fig. 5. Effect of the amount of (a) AIBN and (b) BP on the velocities of the (1) downward and (2) upward waves [46].

66


DAVTYAN et al.

Unfortunately, the data on the effect of error on the value of n are not given in [7, 21, 22], which makes theanalysis of these results difficult.

For example, are the insignificant differences in values 0.32 and 0.34 obtained in the frontal polymerizationof OEDMA under the effect of BP and DCPC, and in values 0.24, 0.25, 0.27, and 0.26 obtained in the frontalpolymerization of TEGDMA the errors of experiment, or can the results be considered reliable? Nevertheless,analysis of the presented data shows that in the frontal polymerization of vinyl monomers, the reaction orderwith respect to the initiator depends on the nature of the initiator and monomer and on the aggregate (liquid,crystalline) state of the monomer. Such dependence of the front velocity on the initial concentration of the ini�tiator cannot be explained within the current theory of frontal polymerization or, moreover, the theory of radicalpolymerization of vinyl monomers.

The experimental and theoretical studies on revealing the reasons for the effect of the nature of the initiatorand monomer on the value of n and clarifying the mechanism of such a phenomenon, unusual for the radicalpolymerization of vinyl monomers, present, aside from pure scientific interest, some methodological interest.In fact, the development of the methods of frontal polymerization will provide additional information on themechanisms of initiation and chain termination at high temperatures that are characteristic for the processes offrontal polymerization.

Regarding the considered data, it is interesting to clarify whether the mentioned regularities remain upon theintroduction of different fine�dispersed and nanoscale additives into acrylamide.

The dependence of the linear rate of frontal polymerization of acrylamide on the concentration of the initi�ator, with the presence in the initial reaction mixture of 30% of bentonite [73], is presented in Fig. 6.

From the data of Fig. 6, the order of the front velocity on the concentration of BP was determined to be ~0.6at the degree of filling of 30%. The reaction orders with respect to the initiators (BP and AIBN) for the polymer�ization of the mixtures of acrylamide with bentonite on the degree of filling were determined in a similar way [73](Figs. 7a and 7b, respectively).

The results indicate the complicated character of the dependence of the reaction order on the concentrationand nature of the initiator. As seen from Fig. 7, the value of n is independent of the direction of the front propa�gation, downward or vice versa. For both initiators, an increase in the amount of filling material leads to anincrease in the value of n. In the case when the frontal polymerization is initiated by BP, an increase in the degreeof filling leads to an increase in the reaction order with respect to the initiator up to 0.61 ± 0.02, while for AIBN,the order increases from 0.38 to 0.58 ± 0.02 [73]. The observed increase of the reaction order with respect to theinitiator to more than 0.5 with the increase in the degree of filling is probably caused by the interaction of poly�acrylamide macromolecules with the surface layers of the filling material and by the occlusion of growing radi�cals by their own macromolecule at the surface of the bentonite layers.

It is interesting that in the frontal polymerization of acrylamide with additives of diatomite, the following val�ues of n were obtained: 0.65 ± 0.02 for BP and 0.6 ± 0.02 for AIBN [73]. The increase in the value of n in the caseof diatomite additives can be explained by the intercalation of the polyacrylamide macromolecules into micro�and nanopores of the diatomite and by their interaction with the pore surface, resulting in the occlusion of activesites in the pores of the filling material.

It can be concluded from the considered data that, for the mentioned filling materials, the termination of thegrowing macroradicals also occurs by a monomolecular mechanism. This fact is the reason for the considerableincrease in the reaction order with respect to the initiator in the frontal polymerization of acrylamide in the pres�ence of bentonite and diatomite.

0.4

4

0 0.2 0.80.6 1.21.0 1.61.4I0, wt %

2

6

v, cm/min

Fig. 6. Effect of the concentration of the initiator (AIBN) on the linear rate of frontal polymerization of a mixture of acrylamide–bentonite. Concentration of the filling material in the mixture, 30% [73].



To reveal the role of the layered or porous structure of the filling materials, similar studies using the same poly�merization initiators were performed for the mixtures of acrylamide with fine�dispersed calcium carbonate [73].The data on the effect of the degree of filling on the reaction order with respect to the initiator are presented inFig. 8.

As in the frontal polymerization of pure acrylamide [46], the reaction orders with respect to BP and AIBNfor the downward and upward thermal waves coincide over the entire range of degrees of filling; however, theirabsolute values differ slightly for each type of initiator. When BP is used as an initiator, the dependence of thepolymerization front velocity on the initial concentration of the initiator for the composites filled with calcium

carbonate (concentration of the filler from 20 to 40 wt %) is described by the equation . With AIBN,the reaction order with respect to the initiator increases, with an increase in the degree of filling to 0.48 (at thedegree of filling of 50 wt %).

The difference in absolute values of the reaction orders with respect to the initiators for mixtures filled withbentonite, diatomite, and calcium carbonate is probably caused by both the structure of the filling materials andthe nature of chemical compounds on the surface layers of bentonite, diatomite, and fine�dispersed calcium car�bonate.

0.43 0.020~u I ±

10

0.4

0

0.2

0.8

0.6

(a)

20 30 40Degree of filling, wt %

10

(b)

20 30 40

n

Fig. 7. Dependence of the reaction order with respect to the initiator in the frontal polymerization of the mixtures of acrylamide–

bentonite on the degree of filling for the ( ) downward and ( ) upward waves, with the use of (a) BP and (b) AIBN as initiators[73].

20

0.4

0 40 503010Degree of filling, wt %

0.2

0.6

n

1

2

1 — BP2 — AIBN

Fig. 8. Dependence of the reaction order with respect to the initiator in the frontal polymerization of the mixtures of acrylamide–calcium carbonate on the degree of filling with the use of (1) BP and (2) AIBN as initiators [73].

68


DAVTYAN et al.

It is interesting to note that, with the use of other filling materials coarser than calcium carbonate (expandedperlite, potassium chloride), the dependence of the front velocity on the concentration of BP and AIBN isdescribed by the regularities obtained for fine�dispersed calcium carbonate.

6. TEMPERATURE PROFILES OF FRONTAL POLYMERIZATION

The temperature profiles, measured by the thermometric or other method in the process of frontal polymer�ization, contain rather interesting information. The temperature profiles measured in practice are usually ofthree main types: one�step, two�step, and three�step profiles containing one, two, and three bends, respectively.

For many processes of frontal polymerization (radical, ionic, polycondensation, etc.), the temperature pro�files are one�step [1, 4, 7, 11, 13, 30, 33, 36, 41, 48] (Fig. 9a). Here, if there is no heat loss from the reaction zoneto the environment, the maximum heating temperature is uniquely related to the conversion rate. Two�step tem�perature profiles of frontal polymerization (Fig. 9b) are obtained in practice in three cases: (1) in the use of amixture of two initiators differing in the activation energies of decomposition [3, 30, 33, 34]; (2) in the combi�nation of initiated and thermal polymerization; and (3) for crystallizing polymers when the exothermic crystal�lization of the resulting polymer begins after complete termination of the polymerization process [3, 8, 9, 46, 47,50, 75] (Fig. 9c).

Three�step temperature profiles (Fig. 9d) are typical for only the frontal polymerization of crystalline mono�mers [9, 46, 47] with the condition that the temperature of the initial reaction mixture is lower than the meltingpoint of the monomer, while the processes of polymerization and crystallization occur successively.

In the two latter cases, the crystallization of the polymer is accompanied by a considerable increase in thedensity of the reaction mixture, which can lead to a loss in the stability of the thermal waves and to the appear�ance of different vibration modes. The loss in stability of stationary frontal modes due to phase transitions, lead�ing to a change in thermophysical properties under conditions of frontal polymerization, is poorly studied.Meanwhile, such investigations considering both parallel and successive processes of polymerization and crys�tallization can play an important role in developing the theory and practice of frontal polymerization.

It should also be noted that the composition of copolymers can be determined by the values of adiabatic heat�ing of the temperature profiles of frontal copolymerization processes [75]. For this purpose, a sufficient differ�ence in thermal effects of the copolymerizing monomers is necessary, in order to ensure that the heat eliminatedin the reaction zone is not consumed in endothermic processes (phase transitions) and the condition of adiaba�ticity of the copolymerization front is fulfilled.

7. ADVANCES IN FRONTAL POLYMERIZATION

7.1. Thermochromic Composites

The dependence of the equilibrium constant of complexation of transition metals with acrylamide is used forsynthesizing polymer composites with thermochromic properties [76, 77]. For this purpose, a homogeneousmixture was prepared of triethylene glycol dimethacrylate with acrylamide and a thermochromic solution con�sisting of CoCl2 ⋅ 6H2O in glycerol, 0.2–3 wt % of AIBN in a total mixture of components. The frontal polymer�ization propagated vertically downward, while the front velocity was determined by visually observing the color

130

Time50

90

210

170

T, °C

(a)

100

Time

75

150

125

T, °C

(b)

Time

(c)

50

175

120

80

160

40

1 2

ΔT, °C

120

80

160

40

ΔT, °C

Fig. 9. Temperature profiles: (a) single�step [3], (b) two�step [47, 93], and (c) three�step [93].



change of the resulting product in the reaction zone. The ratio of initial reagents was varied during experiments.Therefore, solid thermochromic samples in the form of rods that change color in the temperature range of 80–140°С were obtained by means of frontal polymerization [76, 77]. According to the authors, the change in colorwas reversible and could be repeated more than 100 times. The obtained samples of thermochromic compositeswere tested as remotely controlled measuring instruments. The temperature of a hot heat source, measured inthe temperature range of 85–135°С from a distance of 1 m, was determined to the accuracy of 0.5°С. Similarrods obtained with the same composition but under isothermal conditions did not exhibit the correspondingproperties because the components were layered during polymerization.

7.2. Polymer Nanocomposites

The possibility of synthesizing nanocomposites with a uniform distribution of nanoparticles in the polymermatrix is of particular interest. The point is that, because of high surface energy and unusual chemical activity,nanoparticles form larger aggregates in the monomer solution, well in advance of the polymerization process.Therefore, not only do nanoparticles lose their individual properties, but a nonuniform distribution of theagglomerated particles themselves also occurs. The composites obtained in such processes become depleted ofvaluable properties expected from the additives of nanoparticles, and are also known as nonuniform materialswith poor physicomechanical characteristics. Therefore, there is understandably great interest in the interna�tional literature in methods for the deagglomeration of nanoadditives in a monomer medium and in the devel�opment of polymerization modes ensuring the retention of the size and distribution of nanoparticles duringpolymerization, that is, the fixation of a uniform distribution of these additives attained in the monomer mediumfor the polymer matrix. Different methods for the deagglomeration of nanoparticles are known from the litera�ture [78–85]; these include the use of various overlying polymers [78–83] and acoustic fields [84] and the pas�sivation of nanoparticles using approaches for the stabilization of colloid solutions [81]. However, any methodfor passivating nanoparticles with the use of stabilizers leads to another problem: the activity of the nanoparticlesdecreases because of a rather strong interaction between the nanoparticle surface and the stabilizing agent [86–90]. Therefore, in the preparation of polymer nanocomposites, one of the key points is the selection of a thermalmode of polymerization that prevents the agglomeration of nanoparticles during the polymerization processand, thereby, ensures the fixation of the initial uniform distribution of nanoparticles in the resulting nanocom�posite. From the point of view of a uniform distribution of nanoparticles in a polymer matrix, the frontal methodof polymerization appeared to be the most productive and promising method for synthesizing nanocomposites[81, 91, 92].

Indeed, for a reaction mixture containing acrylamide as a monomer, FeO as a nanoadditive, and BP as aninitiator, the use of surfactants enabled the uniform distribution of FeO in the initial reaction mixture, while fur�ther frontal polymerization fixed this state in the polymer matrix [81]. It is known that for nanocomposites ofpolyacrylate–Zr, the conventional sol–gel method of their synthesis leads to an undesirable agglomeration ofnanoparticles in the process of polymerization [91]. The fact is that the precursor of nanozirconia, tetraalkyl zir�conate, is known to hydrolyze so rapidly that the control of hydrolysis in the reactions of polymerization is cru�cial in the synthesis of nanocomposites. Even a chemically stabilized prepared salt of zirconium dioxide is proneto agglomeration in an organic matrix.

It is known that UV initiation, which increases the polymerization rate, can terminate the agglomeration ofnanoparticles. However, even with photoinitiation, large amounts of solvent and stabilizing reagent are requiredfor passivating nanoparticles, which leads to some adverse effects on the properties of the resulting nanocompos�ites. A polyacrylate–nanozirconia nanocomposite was synthesized by frontal photopolymerization with the useof tetrafunctional polystyrene acrylates and tetrabutyl zirconate as a precursor of nanozirconia, respectively [91].In this work, a mixture of an iodonium salt, a protic acid, and tetrabutyl zirconate was used as a photoacidic ini�tiator. The front was directed downward, and the distribution and size of nanoparticles were retained in the rapidpropagation of the reaction front. The frontal mode of polymerization enabled the increase in the concentrationof zirconium dioxide.

To synthesize the nanocomposites of polyacrylamide–FeO and polymethylmethacrylate–SiO2, the methodsof frontal polymerization were also used [92]. In order to stabilize the surface of FeO nanoparticles and to attaintheir deagglomeration and uniform distribution, surfactants were used in [93]. A series of experiments was per�formed in the presence and absence of surfactant additives in order to determine the character of the distributionof nanoadditives throughout both the volume of the initial reaction mixture and the resulting polymer matrix.A photograph of a sample of the system of acrylamide–H2O (20%)–FeO (10%) is presented in Fig. 10, wherethe nonuniform distribution of FeO nanoparticles throughout the volume of the initial reaction mixture is clearlyseen. Upon the addition of 5% of surfactant to this system, the nanoadditives are deagglomerated and distributeduniformly in the volume. It can be seen from Fig. 10b that the presence of a surfactant in the system yields someformations that are uniformly distributed throughout the volume of the initial reaction mixture. The study of this

70


DAVTYAN et al.

mixture with a higher resolution microscope (30× magnification) showed the formation of typical micellar struc�tures (Fig. 10c) whose appearance and development were due to the interaction of the surfactant with the nano�particle surface. The polymerization of acrylamide with the uniformly distributed micellar structures was per�formed at different thermal modes—isothermal, adiabatic, and frontal—under the effect of DCPC (3 ×10⎯3 mol/l) [92].

The obtained samples of nanocomposites were studied using a luminescence microscope. It can be seen fromthe photographs (Fig. 11) that various structures of the polymer nanocomposite are formed depending on thethermal mode of polymerization.

In polymerization in the adiabatic mode, the agglomeration of nanoparticles is observed (Fig. 11a) and thefilling material is distributed nonuniformly in the polymer matrix, which, as noted, is related to the disintegra�tion of micellar structures and, correspondingly, to the agglomeration of released nanoparticles.

In the case of a stationary front (there is no heat loss from the reaction zone to the environment), the nano�particles are distributed uniformly in the polymer matrix (Fig. 11b). This is because the thermal wave of the poly�merization front fixes the distribution of nanoparticles, which finally results in a polymer nanocomposite with auniform distribution throughout the volume of the polymer matrix (Fig. 11b). If there is heat loss, typical layeredstructures are formed (Fig. 11c), which is probably due to variations in the front velocity around its stationaryvalue [11, 12, 93].

The polymerization of acrylamide in the isothermal mode leads to a nonuniform distribution of the nanoad�ditives of FeO in the polymer matrix. Here, one can suppose that heating the reaction mixture to the meltingpoint of the crystalline monomer (~75°С) causes the disintegration of micellar structures and, therefore, theagglomeration of the FeO nanoparticles.

(а) (b) (c)

Fig. 10. Initial reaction mixture (a) without surfactant and (b and c) in the presence of surfactant; (c) photograph taken at 30×magnification [92].

(а) (b) (c)

Fig. 11. Effect of the thermal mode of polymerization on the structure of polyacrylamide�based nanocomposites obtained in the(a) adiabatic mode, (b) stationary frontal mode, and (c) nonstationary mode [92].



Nanocomposites of polymethylmethacrylate–SiO2 were also synthesized with different concentrations of theSiO2 nanoparticles 10 nm and 0.6 and 30 μm in size [92].

It was shown in [81, 82] that the relative heat capacity of nanocomposites obtained by the emulsion polymer�ization of methylmethacrylate in the presence of different amounts of SiO2 nanoadditives did not obey the addi�tivity law. This fact was explained by a rather strong interaction between the polymer chains and the nanoparticlesurface, resulting in the formation of a rigid amorphous fraction (RAF) on the nanoparticle surface. Here, thepresence of RAF increases by 5–6°C the glass�transition temperature of the synthesized nanocomposites [80,81, 84, 85]. The formation of RAF was earlier proved for various polymerizing mixtures with nanoscale fillingmaterials of different nature [80, 86]. It is interesting to compare the formation of RAF for filling material par�ticles of different sizes; therefore, the thermophysical properties of polymer composites with the SiO2 additiveswith an average particle size of 10 nm and 0.6 and 30–50 μm were studied.

The dependence of the relative heat capacity on the amount of added nanoscale filling material is presentedin Fig. 12 [92]. As seen from the data, the addition of SiO2 particles with an average particle size of 30–50 μminto the system leads to an additive change in the relative heat capacities of the polymer and SiO2 (Fig. 12,curve 1). This can indicate that there is no chemical interaction between the surface of the filling material andthe macromolecules of polymethylmethacrylate or that its contribution is insignificant because of a low surface�to�volume ratio for large particles. The decrease in the size of the filling material to 0.6 μm leads to the changein the shape of the dependence of the value on the amount of filling material (Fig. 12, curve 2).

The ratio of decreases more rapidly than curve 3; even at degrees of filling of 15–20 wt % ormore, curve 2 becomes parallel to linear curve 3. The use of nanoparticles (10 nm) leads to a sharper dependenceof the ratio of on the added amount of nanoparticles (curve 3). In this case, the section of par�allel changes in relative heat capacities is observed at even larger degrees of filling (30–35 wt %). The characterof the dependence of on the degree of filling obtained for systems with nanoparticle sizes of 0nm and 0.6 μm (curves 1 and 2) indicates that there is a rather strong interaction between the macromoleculesof the polymer binder and the nanoparticle surface. The observed smaller deviation of this dependence for par�ticles with an average size of 0.6 μm is due to a lower concentration of the nanoscale fraction of SiO2 in the initialpowder.

According to the data of Fig. 12, the thickness value of RAF determined for SiO2 nanoadditives with a particlesize of 10 nm was ~(2.3–2.5) nm, while for particles with an average size of 0.6 μm it was ~(0.5–0.7) nm [92].

It was shown that for the nanocomposites of polymethylmethacrylate–SiO2 obtained by different methods ofpolymerization, such as emulsion (in the presence of surfactants) and microemulsion (under the effect of high�frequency acoustic fields), the thickness value of RAF was 2–2.3 nm [83–85]. The similar value of the RAFthickness for the nanocomposite samples obtained by the frontal polymerization of methylmethacrylate in the

form polp pC CΔ Δ

form polp pC CΔ Δ

form polp pC CΔ Δ

form polp pC CΔ Δ

20

0.4

0

0.2

0.8

0.6

1.0

1

2

3

ТАФ

40 60 80 100SiO2, wt %

Δсp form/Δсp pol

Fig. 12. Dependence of the value of ΔCp form/ΔCp pol on the amount of SiO2 added to the polymerization medium. Particle size:(1) 10 nm, (2) 0.6 μm, and (3) 30–50 μm [92].

72


DAVTYAN et al.

presence of SiO2 with a nanoparticle size of 10 nm indicates that the thermal wave leads to the deagglomerationof particles, while the polymerization zone, following the heating zone, fixes this state. It is obvious that at higherdegrees of filling with the SiO2 nanoparticles (more than 30–35 wt %), only partial deagglomeration of largerparticles occurs under the effect of the thermal wave.

The parallel section of curves 1, 2, and 3 (Fig. 12), as noted above, can be explained by the agglomeration ofnanoparticles, preventing the interaction of the binder macromolecule with the nanoparticle surface [92]. Inorder to prove this assumption, nanocomposite samples with different concentrations of SiO2 (10 nm) were stud�ied using a transmission microscope. The results are presented in Fig. 13.

It can be clearly seen that, up to degrees of filling of 30–35%, the SiO2 nanoparticles are uniformly distributedin the polymer matrix (Fig. 13a). The increase in the concentration of nanoscale filling material to 40% causesthe agglomeration of particles (Fig. 13b), and the further increase in the concentration of SiO2 particles to 45%or more considerably affects the sizes of the agglomerated particles (Fig. 13c).

The changes in the dynamic modulus of elasticity (Е '') and in the slope of mechanical losses (tanδ) on tem�perature for nanocomposites of polymethylmethacrylate–SiO2 with a different concentration of SiO2 (10 nm)are presented in Figs. 14a and 14b [92].

The analysis of the dependence of Е '' on temperature (Fig. 14a) shows that an increase in the quantity ofnanoscale filling material to 30–35% leads to an increase in the dynamic modulus (curves 1–3), and at a degreeof filling of more than 35% the value of Е '' becomes almost independent of the SiO2 additives (curve 4). Theobserved expansion in the region of glass�transition temperature (curves 1–3) indicates the formation of RFAon the surface of SiO2 particles. These results are proved by the data on the effect of the amount of SiO2 on theslope of mechanical losses. In fact, it follows from the data of Fig. 14b, curves 1–3, that the temperature rangeof main mechanical losses is related to the devitrification of the polymer binder of the nanocomposite. Here, theincrease in the amount of SiO2 to 30–35% leads to the broadening of the peaks of mechanical losses, to theirshift to the higher temperature region, and to the increase in maximum values. The observed increase in peaksand their shift to the higher temperature region, as noted, are the result of a rather strong interaction of thebinder macromolecules with the grain surface of the filling material, resulting in the formation of RAF.

However, in the curves of main mechanical losses (Fig. 14b), the secondary transition in the temperaturerange of ~140–190°С for nanocomposite samples with the degree of filling of 30% or more remains unex�plained. The presence of such a secondary transition as a component of the main peak of the slope of mechanicallosses was also noted in [87, 94], where this was associated with the secondary glass transition of polymer nano�composites.

Apparently, the occurrence of the secondary transitions observed in Fig. 14b can be explained by the fact thatsingle macromolecules participating in the formation of RAF can bond the SiO2 nanoparticles, resulting in theformation of structures resembling three�dimensional networks [95].

Thus, the following conclusions can be drawn on the basis of the results of [91, 92]:(1) Frontal polymerization is a positive technological factor contributing to the deagglomeration of particles

in a monomer medium and to the fixation of the uniform distribution of nanoparticles in the resulting polymercomposite.

(2) In the process of frontal polymerization, a rather strong interaction of the polymethylmethacrylate mac�romolecule with the nanoparticle surface is observed. As a result, RAF is formed at the interfacial boundary,causing a considerable change in the relative heat capacity, glass�transition temperature, and dynamic mechan�ical properties of nanocomposites in dependence on the degree of filling.

40 nm(а) (b) (c)

500 nm 1 μm

Fig. 13. Microphotographs obtained by (a and b) transmission microscopy and (c) electron microscopy: (a) the uniform distri�bution of SiO2 nanoparticles and (b and c) their agglomeration in the polymer matrix [92].



7.3. Synthesis of Intercalated Superconductive Polymer�Ceramic Nanocomposites

In order to obtain superconductive polymer�ceramic intercalated nanocomposites containing transitionmetals Mn, Co, Zn, and Ni, metal�complex monomers of a general structure Me(AAm)4 (NO3)2 (AAm, acry�lamide) were polymerized in the frontal mode in the presence of different quantities of superconductive ceramicmaterial Y1Ba2Cu3O6.97 [96, 97].

The results of the investigation of the superconductive and physicomechanical properties of the Mn�, Co�,Zn�, and Ni�containing polymer�ceramic nanocomposites are presented in Table 1. It can be seen from the tablethat the beginning (Тs) and the end (Tf) of the superconductivity transition are shifted to the higher temperatureregion with respect to the initial ceramic material (Тs = 92 K and Tf = 78 K). The value of Tb shifts by 1–3 K; Tf,by more than 5 K. The increase in the Тs value by 1–3 K was shown to be related to the intercalation of the ele�ments or fragments of the polymer binder into the interlayer space between ceramic grains [98].

The intercalation of the fragments of the binder macromolecules into the interlayer space between ceramicgrains affects not only the superconductive and physicomechanical properties but also the formation of the mor�phology of the interfacial structure and the thermophysical and thermochemical properties of polymer�ceramicnanocomposites [98].

It is interesting that nanoadditives of silver or aluminum (5 wt % of the total binding mass) lead to the forma�tion of current�conductive nanocomposites with a current density of up to (3–5) × 103 A/cm2.

7.4. Interpenetrating Polymer Nets

The synthesis of interpenetrating three�dimensional polymer net structures by conventional methods israther complicated but suitable for limited types of monomers. The obtaining of such net structures by a two�stage process is the most widespread method. At the first stage, a three�dimensional polymer is obtained by rad�ical or ionic polymerization or by polycondensation; then, a particularly selected monomer is added, which pen�etrates the three�dimensional network under certain conditions, polymerizes itself, and causes the network toswell. As a result, two polymers are formed with rather uniformly cross�linked fragments of interstitial chains.

Another method is related to the simultaneous polymerization of two multifunctional monomers. Obviously,the differences in the polymerization rate create certain (often, principal) difficulties in this case; therefore,either the corresponding temperature is selected or the methods of photopolymerization are used. Therefore,considering that frontal polymerization is a high�temperature and rapidly propagating process, interpenetratingthree�dimensional polymers were synthesized under conditions of the propagation of thermal polymerizationwaves [99]. For this purpose, the simultaneous frontal polymerization of a mixture of monomers of triethyleneglycol dimethacrylate with bisphenol diglycidyl ether was performed. The monomers were thoroughly mixedwith a complex of alkyl amine with boron trichloride (BCl3NR3) and with the following initiators: 1,1�di(tert�butylperoxy)�3,3,5�trimethylcyclohexane and tert�butyl hydroperoxide. During the process of frontal polymer�ization, the temperature profile and the dependence of the front velocity on the initial ratio of the monomerswere measured [99]. The temperature profile of frontal polymerization was characterized by one bend, which

60

10

020 100 140 180 T, °C

5

15

60

2

020 100 140 180 T, °C

1

3

E '' × 103, MPa

(a)4

3

2

1

4

tanδ

(b)

4

3

2

1

Fig. 14. The change in (a) the dynamic modulus of elasticity and (b) the slope of mechanical losses on temperature. The degreeof filling (% of SiO2 from the weight of the monomer): (1) 0, (2) 20, (3) 30, (4) 45 [92].

74


DAVTYAN et al.

indicated the presence of only one polymerization wave. In the opinion of the authors, this is evidence of theobtaining of interpenetrating three�dimensional structures. Indeed, investigations of opaque colored samples bythe methods of scanning and transmission electron microscopy did not reveal the phase layering. On the basis ofthe results, the authors concluded that this method should be particularly effective for the obtaining of large sam�ples [100]. Furthermore, the methods of frontal polymerization were used for synthesizing interpenetratingpolyacrylamide–polyacrylamide hydrogels [100].

7.5. Functionally Gradient Materials

Polymer gradient materials were synthesized for the first time using the methods of frontal polymerization[38], where the dye was distributed over the length of a sample according to a predetermined parabolic law. Forthis purpose, a mixture of tri�(ethylene glycol)�dimethacrylate (TEGDMA) with the initiator (tricaprylmethy�lammonium persulfate) at a certain concentration and the same reaction mixture plus the dye (phthalocyaninealuminum chloride) were prepared in separate vessels.

In order to perform the reaction, frontal polymerization was initiated in the bottom part of a test tube 14 mmin diameter. After the stationary state of the reaction was attained, both the monomer with the initiator and themixture of the dye with the monomer and the initiator were supplied to the reaction zone using two pumps. Therate of both flows was set so that, in the total mixture of components, the parabolic law of the dye supplied to thereaction zone was obeyed over the reactor height. The temperature profiles were measured by a thermocoupleplaced in the central part of the reaction ampoules, while the front velocity was determined by visually observingthe travelling of the reaction zone.

The obtained materials with a predetermined law of dye distribution over the sample height were recorded byvideo methods, which completely corresponded to the expected results. The region without dye was set to thebrightness level with a zero dye concentration, while the region with the maximum concentration was set to themaximum dye concentration.

The typical temperature profiles have a two�step structure. Here, a plateau is observed in the temperaturerange of ~(75–80)°С, after which the temperature grows to the limiting value of ~(190–200)°С. The presenceof such a temperature plateau corresponds to a layer of unreacted liquid monomer situated just above the poly�merization front. In the opinion of the authors of [102], the reason for this is intensive convection occurringbecause of the flows of the reaction mixture components supplied to the reaction zone. From our point of view,complex temperature profiles with two bends and the formation of the temperature plateau can be of a purelychemical nature. For example, the complexation between the dye and the initiator can take place, resulting in

Table 1. Superconductive and physicomechanical characteristics of Mn�, Co�, Zn�, and Ni�containing polymer�ceramicnanocomposites

Composition of nanocomposites

Nature of metal

Pressing time, min Тс, К ΔТ, К σ, MPa Е ×10–3

MPa ε, %Y1Ba2Cu3O6.98Metal�complex

monomer

g wt % g wt %

0.293 43 0.388 50 Mn 10 5 0 – – –

0.396 50 0.396 70 Mn 5 4 8 – – –

0.90 70 0.29 30 Mn 5 4 1 15 4.55 3

0.518 73 0.196 27 Mn 5 3 0 – – –

0.416 67 0.209 33 Mn 10 4 10 – – –

0.552 78 0.156 22 Mn 5 5 8 – – –

0.325 51 0.318 49 Co 5 3 0 – – –

0.432 60 0.283 40 Co 5 2 8 – 2.40 –

0.503 70 0.228 30 Co 2 2 17 4.2 5

0.90 70 0.390 30 Zn 5 5 15 – 4

0.416 67 0.209 33 Zn 10 4 – 3.10 –

0.552 78 0.156 22 Zn 5 5 – – –

0.486 70 0.208 30 Ni 5 5 14 2



two forms of the initiator. In this case, the formed initiators (initial tricaprylmethylammonium persulfate andcomplex), as shown in paragraph 6, can cause stepped configurations in the temperature profiles of the frontalpolymerization of TEGDMA, due to the difference in the activation energies of decomposition.

Thus, on the basis of the results of [38], one can conclude that frontal polymerization enables the synthesisof polymer materials and composites with a predetermined distribution of not only optical properties but alsochemical composition or functional groups over the radius or length of the sample, which is of obvious practicalvalue for the purposeful regulation of polymer properties.

7.6. Polymerization in Laminar Flows

Polymerization at the propagation of the front of thermal waves occurring in periodic systems has both meth�odological and practical value as a simpler method for synthesizing polymer materials difficult to obtain by con�ventional methods. Frontal polymerization becomes particularly important if implemented under continuousconditions. It seemed that such a process could be easily implemented in tubular reactors, where the flow of ini�tial reacting substances is perpendicular to the surface of the reaction front. However, it should be noted herethat, depending on the nature of the monomer, the polymerization rate, the aggregate state of the resulting poly�mer, and other factors, the process can meet principal difficulties. Therefore, it is more suitable to consider thisregarding the classification of monomers for frontal polymerization, discussed in paragraph 4.

It is obvious that frontal polymerization can be easily implemented in continuous tubular reactors for mono�mers of the first group. The point is that, in the synthesis of thermoset materials in frontal polymerization at thelaminar flow of the initial reacting mixture, the relative position of any two fixed points is not changed; that is,the movement of the monomer mixture occurs according to the law of piston motion. This means that the reac�tion times for the conversion products are the same, which ensures good properties of the obtained materials.Certainly, some questions arise here—requiring additional investigation in each case—related to the dissipationof the energy of dry friction and the adhesion of three�dimensional polymers to the reactor walls.

To confirm the abovementioned, frontal solidification in a continuous tubular reactor was theoretically cal�culated and experimentally implemented to obtain profiled products of carbon fiber�reinforced and glass fiber�reinforced plastics [101–103]. The conditions for obtaining the stationary thermal modes were found, the sam�ples were obtained in tubular form, and their main physicomechanical properties were determined [101–103].

Probably, frontal polymerization in continuous tubular reactors can also be implemented for crystallinemonomers (the third group), if the initial powder mixture is supplied to the reactor according to the law of pistonmotion. It is obvious here that, independent of the aggregate state of the resulting polymer, there is no velocitygradient in a powder monomer, which provides some prerequisites for implementing this process.

In general, monomers from the second and fifth groups cannot be polymerized in continuous tubular reac�tors. In fact, the adhesion of a high�viscous polymer mixture to the walls and the presence of the velocity gradientover the radius lead to the formation of a rather extended stream of liquid monomer (in the axial part of the reac�tor), which reaches the reactor outlet and leaves it unreacted [104]. Polymerization of monomers from thesegroups in continuous tubular reactors of frontal polymerization possesses other considerable drawbacks, such asdifferent reaction times and the formation of the polymer in significantly nonuniform temperature fields. Thesefactors worsen the molecular�weight characteristics and, therefore, the properties of the resulting polymer.

However, it should be particularly noted that, in a number of cases, thermoset polymers can be synthesizedin continuous tubular reactors under conditions of frontal polymerization. For example, if the temperature oflimiting heating of polymerization thermal waves is lower than the melting point of semicrystalline polymers orthe glass�transition temperature of amorphous polymers, the flow of liquid monomer, similarly to the monomersof the first group, will follow the law of piston motion. Such an investigation was performed using the exampleof the anionic frontal polymerization of ε�caprolactam with consideration for the dry friction of polycrystallinepoly�ε�caprolactam with the reactor walls [105]. The experimental data were compared with the theoreticalresults obtained in [5].

Polymerization processes in continuous tubular reactors were also studied in [106–110].It should be noted that, for thermoset polymers, reactors of frontal polymerization with radial symmetric

flows of initial substances and products, in particular reactors with cylindrical symmetry, should have a definiteadvantage over tubular reactors (Fig. 15).

The polymerization of monomers of the fourth group can be effectively implemented in tubular reactors withturbulent flows. This important question will be discussed below.

The frontal polymerization of methylmethacrylate in a 4.6�l cylindrical reactor was studied in [33, 34, 111];a schematic diagram of the reactor is presented in Fig. 15.

In order to investigate the possibility of frontal polymerization of methylmethacrylate in cylindrical (Fig. 15)and spherical reactors with radial symmetric flows, a specially designed facility with a frontal polymerization

76


DAVTYAN et al.

reactor was developed at the Branch of the Institute of Chemical Physics of the Soviet Union Academy of Sci�ences (now the Institute of Problems of Chemical Physics) in 1988 [30, 31]. With the goal of technologicalimplementation of the process, the frontal polymerization of methylmethacrylate was studied in the cylindricalreactor with radial symmetric flows under the effect of different initiators such as DCPC, BP, TBP, and theirmixtures. The results were partially published as preprints [30] and articles [33, 34, 111].

The temperature profiles obtained in the polymerization process in the cylindrical reactor at pressures of upto 15 atm are presented in Fig. 16.

At low feed rates, the temperature along the reactor radius slowly increases (curve 1) because of the smallamounts of reaction mixture entering the reactor; here, polymerization takes place throughout the entire reactorvolume with different rates. With an increase in the flow rate (Fig. 16, curves 2 and 3), the quantity of active reac�tion mixture grows, which increases both temperature and the reaction rate. At a flow rate of 3–3.5 l/h or more,a stationary mode of frontal polymerization is attained in the reactor. Therefore, further increase in the con�sumption of the reaction mixture leads to the parallel transfer of thermal polymerization waves along the radialdirection to the reactor outlet (Fig. 16, curves 5–8). The dependences of the heating temperature and the con�version rate on the flow rate of the initial reaction mixture are presented in Fig. 17.

As seen from the data of Fig. 17, with an increase in the flow rate the increase in the maximum temperaturecontinues to grow, up to values at which the initiator is completely exhausted in the reaction zone. Furtherincrease in the flow rate does not affect the maximum heating temperature (Fig. 17, horizontal section of curve1), while the location of the reaction zone moves away from the center to a distance proportional to the con�sumption (Fig. 17, linear section of curve 2). With feed rates of 3 l/h and on, the reactor curvature does not affectthe structure of the temperature profiles or the limiting heating temperature; therefore, one can consider thepolymerization front is set in the reactor with a close to flat geometry.

16 7 8

2

3

4

5

3

5

9

Fig. 15. Schematic diagram of a cylindrical reactor of frontal polymerization: (1) stub for introducing a mixture of monomer andinitiator into the reactor, (2) perforated tubular surface, (3) molten polymer with residual monomer, (4) the surface of the poly�merization front, (5) electrical heaters, (6–8) capillary metallic tubes for mobile thermocouples, and (9) valve for maintainingthe pressure drop [33].



In the set stationary mode, independent of the feed rate, the conversion rate is ~0.4, the value reaches3.5 × 104, and the polydispersity decreases from 7 to 3–3.2. The variation in the initial concentration of DCPCand in the flow temperature does not considerably affect the yield or the MWD characteristics of the polymer.

The rather wide molecular�weight distribution under conditions when there is almost no gel effect isexplained by a complete exhaustion of the initiators in the reaction zone, a decrease in the concentration of mac�roradicals, and an increase in their lifetime. Consequently, in the time when the molten polymer occurs withinthe reactor, a high�molecular fraction is formed yielding an increase in the polymer polydispersity. The use of

the mixtures of DCPC, BP, and TBP leads to an increase in the conversion rate (~0.7) and value (~4 × 104)and to a decrease in polydispersity to ~3 [33]. To regulate the conversion rate and the MWD characteristics, athree�stage process of radical polymerization was studied by analytical and numerical methods [34], with con�sideration of the equation of heat conductivity and radial symmetric flows of initial substances and products. Itwas shown that a significant increase in the final conversion rate is determined by two factors: (1) the use of themixtures of two initiators different in activation energies of decomposition and (2) the addition into the initialreaction mixture of small amounts of polymer [34]. Therefore, the frontal polymerization of methylmethacry�late in the cylindrical reactor was performed under the effect of a mixture of DCPC and TBP in the presence of10–13% of polymethylmethacrylate (number�average molecular weight, 7 × 104) predissolved in methyl�methacrylate.

The results of the effect of the feed rate on the value of limiting heating (ΔТ), the conversion rate, the num�ber�average molecular weight, and polydispersity of the resulting polymer are presented in Table 2.

nP

nP

2

50

4 6 8 r, cm

75

100

125T, °C

1

234

5 6 7 8

0

Fig. 16. Temperature profiles of the frontal polymerization of methylmethacrylate initiated by 0.015 mol/l DCPC, at the feed rateof the reaction mixture of (l/h) (1) 0.5, (2) 1, (3) 2, (4) 2.5, (5) 6, (7) 12, (8) 20, and (9) 40 [33].

5

60

0

40

80

8

4

12

10 15 20 40

ΔT, °C rlim, cm

Fig. 17. Effect of the feed rate of the reaction mixture on (1) the maximum heating temperature and (2) the coordinate of thepolymerization front [33].

78


DAVTYAN et al.

It can be seen from the data of Table 2 that the initiation of the frontal polymerization of methylmethacrylateby the mixture of DCPC and TBP and the addition of the polymer increase the conversion rate to 90–93%.It should be noted that the increase in the conversion rate, in its turn, is beneficial for the molecular�weight char�acteristics of the resulting polymer.

Therefore, the results of [33, 34] allow the conclusion that in the radical frontal polymerization of methyl�methacrylate in a flow�through cylindrical reactor with radial symmetric flows, a polymer can be obtained withthe required conversion rate and satisfactory molecular�weight characteristics. However, as mentioned in [34],“One of the main issues related to the performance characteristics remains open, namely, the stability of thereactor in dependence on different perturbations arising during its operations.”

The factors affecting the stability of thermal polymerization waves can be external, like random fluctuations,the flow temperature, or the reactor walls, and internal, related to the formation of dead zones and gravitationalconvective mass transfer in the reactor.

In order to reveal the presence of dead zones in the reactor and the increase in their lifetime, the frontal poly�merization of methylmethacrylate (under the effect of a mixture of DCPC and TBP with additions of 10% poly�methylmethacrylate) was performed for 40 h at a constant feed rate [111]. During the process temperature wasmeasured at three selected points along the reactor height, and the thermocouple readings were recorded in dif�ferent time intervals (5, 12, 25, and 40 h). The readings were constant, which allowed us to conclude that thepresence of radial symmetric flows prevents both the formation of dead zones and the convective mass transferof the molten polymer from the reaction zone to the monomer solution. A study of the stability of thermal auto�waves at low consumption showed that, from the feed rate of 1.5 l/h, damping vibration modes appeared; furtherdecrease in the feed rate caused the formation of periodic vibrations of constant amplitude [111]. On the basisof theoretical investigations of frontal polymerization in reactors with radial symmetric flows, one� and two�dimensional losses in stability were determined earlier [102], with the appearance of corresponding vibrationand spin modes. The damping vibrations of the polymerization front also arise with a sharp change in consump�tion; however, such hydrodynamic vibrations relax rapidly to the setting of a new stationary state in the system.

Considering the linear dependence of the front coordinate on the consumption value (Fig. 18, curve 2), a pre�requisite was obtained ensuring the stability of the frontal modes of polymerization to the perturbations arisingin the fluctuations in the feed rate [111]. However, since the loss of stability in the stationaryfrontal modes can also occur through heat loss from the reactor walls to the environment, it was shown that the

condition < 4, obtained for the frontal polymerization of methylmethacrylate in acylindrical reactor with radial symmetric flows, completely ensured the stability of the reactor operations [112].

In the above expressions, rп is the value of the coordinate of the reaction front when the front shape can beconsidered flat; r, v, and u are the front coordinate, the front velocity, and the feed rate; r0 and r1 are the initialand final values of the reactor radius corresponding to the radial symmetric propagation of the reaction mixture;E, Ta, and T0 are the efficient activation energy of the polymerization reaction, the temperature of adiabaticheating, and the temperature of the flow; and R is the gas constant.

The cylindrical reactor with radial symmetric flows, 4.6 l in volume, was developed in a research and produc�tion association in Perm, Russia.

7.7. Polymerization in Turbulent Flows

Earlier, polyisobutylenes of different molecular weight were synthesized under industrial conditions, whenpolymerization was performed in stirred�tank reactors of large volumes and at large temperature gradients,

1 0nr r u br r< <v

( )2

0 2 4a aZ E T T RT= − <

Table 2. Effect of monomer consumption on the characteristics of the frontal polymerization of methylmethacrylate in thepresence of a mixture of initiators

No. Flow rate, l/h [DCPC] + [TBP], mol/l

Quantity of added polymer

ΔТ, °С Conversion rate × 10–4

1 3.5 0.0073 + 0.0043 10 195 0.92 5.4 2.42 6.0 0.0073 + 0.0043 10 191 0.90 5.5 2.33 6.0 0.0073 + 0.0043 0 146 0.68 4.2 2.84 8.0 0.0073 + 0.0043 10 195 0.92 5.4 2.35 12 0.0073 + 0.0043 13 196 0.93 4.9 2.36 20 0.0073 + 0.0043 10 195 0.92 5.4 2.37 6.0 0.005 + 0.005 10 194 0.91 7.9 2.2

Pn Pw/Pn



which caused instability of the process, low product yields, and poor molecular�weight characteristics of theresulting polymer. Therefore, the macrokinetic characteristics of the cationic polymerization of isobutylene in atubular reactor were investigated experimentally and theoretically [49–61].

The experiments were performed on an apparatus enabling the regulation of the linear velocities of the flowsof reagents to the reactor, the measurement of the process temperature, and the control over changes in selectedpoints of the reaction volume [49–54, 56, 57, 59, 61]. Sample collection from different reactor zones allowedthe quantification of the formed polyisobutylene and the study of the dependence of molecular�weight charac�teristics on the concentrations of the monomer (a solution of isobutylene in heptane), the catalyst (C2H5AlCl2),their feed rate, and the size of the conversion zone.

According to the data of [49–54, 56, 57, 59, 61], the highest polymerization rates are observed at the pointof addition of the catalyst, while the lowest rates are near the reactor walls; the main fraction of the polymer (50–70%) forms in the zone of introduction of the reagents for 1–2 s. With an increase in the concentration of themonomer in the initial mixture, a decrease in the molecular weight of the polymer and in the conversion rate isobserved. With a fixed reagent feed rate (1.5 m s–1) and constant monomer concentration (12 wt % in the initialmixture), the temperature and the conversion rate increase while the molecular weight of polyisobutylenesharply drops with increasing distance from the point of introduction of the reagents. The observed experimentalfactors are related to an increasing amount of heat elimination during polymerization, deteriorated heat transfer,and an increase in the reaction rate of chain transfer to the monomer [49–54, 56, 57, 59, 61]. The functions ofMWD for different experiments are presented in Fig. 18 in semilogarithmic coordinates [49–54, 56, 57, 59, 61].Comparative analysis of curves 1–8 (Fig. 18) shows that the broadening of the MWD is caused by the formationof significant amounts of low�molecular polymer fraction along the reactor length.

It is supposed on the basis of the results of [49–61] that, topochemically, the reaction of the polymerizationof isobutylene belongs to the class of rapid processes, while the reaction zone itself, analogous to combustionprocesses, is the “torch” of the chemical reaction.

Considering the real values of the linear flow velocities, the density of the reaction zone and its dynamic vis�cosity coefficient, and the inner diameter of the tubular reactor, the value of the Re criterion was evaluated(~104) [49–52, 59–61]. This allows the use of a constant coefficient of turbulent diffusion ( ) equal to the tem�perature conductivity coefficient for the studied tubular reactor as coefficients of mass and heat transfer

, where λT, с, and ρ are the mean values of the heat conductivity coefficient, heat capacity, and thedensity of the reaction mixture, respectively. In subsequent works, more accurate models of the chemical reac�tion of polymerization in turbulent flows were used by solving the Navier–Stokes equations together with theequations of chemical kinetics and a two�parameter q–ε approximation used for the turbulent mode [51–56].

The kinetic mechanism of the cationic polymerization of isobutylene is presented by the following reactions[49–52]:

K + M A*

A* + M

TD

T TD c= λ ρ

Ku

Kp *nA

1

–1

123

4

5

678

2 3 4 5 6j × 10–3

0

1

logPn( j)

0

Fig. 18. Semilogarithmic anamorphisms of the MWD function of polyisobutylene (the concentration of the monomer, 12 wt %)along the reactor length (m): (1 and 5) 0.02, (2 and 6) 0.1, (3 and 7) 0.3, and (4 and 8) 0.48; and the concentration of the monomer(wt %): (5) 5, (6) 10, (7) 17, and (8) 20. The feed rate of the reagents, 1 m s–1 [49].

80


DAVTYAN et al.

Pn

+ M A* + Pn .

In the above reactions, K is a catalyst; and are active sites in the stages of chain initiation and propa�gation; is a dead macromolecule; and Ku, Kp, Kr, and KM are the rate constants of initiation, propagation, ter�mination, and chain transfer to a monomer, respectively.

It is assumed for the molecular�weight characteristics of the resulting polyisobutylene that the molecularweight of polyisobutylene is determined in a wide temperature range by the reaction of chain transfer to themonomer . Therefore, the MWD of the polymer at a given temperature is an exponential function:

.

It follows from the last equation that the MWD of polyisobutylene is determined by the intensity of the tem�perature effect on the value of , that is, the difference in the activation energies of the chain transfer to themonomer and the chain propagation EM – Ep.

Numerical analysis of the differential equations describing the process of rapid cationic polymerization ofisobutylene in a reactor with turbulent flows, regarding and disregarding the contribution of longitudinal diffu�sion with respect to М, А*, and Т, yielded the distribution of temperatures, the concentrations of the monomerand the catalyst (Fig. 19), the weighting function (ρw( j)) of the polymer MWD at the reactor outlet (length l andradius R), and four moments of MWD (zeroth, first, second, and third).

Figure 19 demonstrates a typical distribution of the temperature and concentration of the monomer and cat�alyst over the reactor volume [49–52, 65, 66]. It can be seen from the data of Fig. 19 that the polymerizationprocess is mostly concentrated in the zone of introduction of the catalyst, which completely corresponds toexperimental data [49–52].

The temperature and rate of polymerization depend considerably on initial reagent concentrations and value and weakly depend on heat transfer coefficient h. The maximum rate of polymerization is observed near the

zone of introduction of the catalyst, and the rate decreases with increasing distance from this zone, which affectsboth the yield and the molecular�weight characteristics of polyisobutylene. The increase in the coefficient ofheat transfer to the environment, while all other parameters are constant, leads to some decrease in the temper�ature extremes in the reaction zone and, therefore, to a slight narrowing of MWD.

The temperature distribution and absolute value of the temperature extremes in the reaction zone are deter�mined by the polymerization rate and, therefore, by the concentrations of the monomer and the catalyst. Anincrease in the concentration of the monomer leads to a considerable broadening of MWD because of the for�mation of a low�molecular polymer fraction. An increase in the initial concentration of the catalyst gives a sim�ilar effect. Comparison of the result of numerical solution and the experimental data shows their qualitative andquantitative agreement [49–52]. An important consequence of the results is the formation of a local reactionzone, a torch, whose volume is significantly less than the dimensions of industrial reactors; this is the reason forthe breakthrough of the monomer along the reactor walls, their low performance, and inefficiency. The depen�dence of the yield of polyisobutylene and its molecular�weight characteristics on the geometric dimensions ofthe reaction zone (length l and radius R) is a consequence of the formation of different thermal diffusion modes[49–64] and the ultrarapid polymerization of isobutylene in turbulent flows.

The results of numerical solution and some experimental data on the effect of the radius of the reaction zoneon conversion, the number�average degree of polymerization, and the polydispersity of polyisobutylene are pre�sented in Table 3 [49–52, 65, 66].

In the topochemical aspect, three types of thermal diffusion–macrokinetic modes are distinguished: A, B,and C [49–52].

For small radii R (mode А), active sites are rather uniformly distributed in a radial direction, which is thereason for the uniform temperature distribution in the reaction zone. This situation leads to the formation of sta�tionary frontal polymerization modes with flat surfaces of the concentration A*, М, and temperatures perpen�dicular to the axis of the reaction zone. Mode B is characterized by the formation of the torch without monomerbreakthrough and corresponds to the formation of a curved reaction front or torch without the breakthrough ofunreacted monomer. Here, the conversion slightly decreases; a decrease in the number�average degree of poly�merization and an increase in polydispersity ( ) are observed. Another macrokinetic mode, “localtorch,” is formed at relatively large values of R (mode C) [49–52, 65, 66]. In this mode, the active sites are ter�minated, having had no time to diffuse to the peripheral zones of the reaction volume, which is the reason forthe breakthrough of unreacted monomer between the torch boundary and the reactor wall. Macrokinetic mode

*nAKr

*nAKM

*A *nA

nP

p МnP K K=

( ) 1 expnn n

jjP P

⎛ ⎞ρ = −⎜ ⎟⎝ ⎠

nP

TD

*A

2w nP P >



C is characterized by complicated concentration–temperature fields (М, A*) [49–52]. The dimensions of thelocal torch are determined by the ratio of two competitive processes: the mixing of concurrent flows (the mono�mer with a solvent and active sites) and the termination of active sites A*.

For ultrarapid reactions in turbulent flows, the formation of frontal modes is a general phenomenon, whichis evidenced by the results of experimental and theoretical investigations of the bimolecular reaction of KSCNwith FeCl3 in turbulent flows [53–55]. The frontal mode and the geometric shape of the wave were determinedby the boundary of coloration in the interaction of KSCN with FeCl3 by photographic and video methods [53–55]. One of the reagents is introduced radially into the reactor using the external surface of the reactor; the pointof introduction is considered the beginning of the reactor along the flow axis. Another substance is supplied tothe reactor by two means: either along the flow (method A) or in a radial direction (method B) through specialopenings in the stub. The point of introduction of substance 1 can coincide with the beginning of the reactor, orit can be behind or ahead of the beginning of the reactor by distance l. Then, the expressions A(0), В(0), A(–l),В(–l), A(+l), and В(+l) mean that both the axial and radial supplement of substance 1 are performed at thebeginning of the reactor (0), behind the beginning by distance l (–l), and so on. Depending on the method bywhich substance 1 is introduced and the linear flow velocities V1 and V2, the formation of three frontal modesprincipally different in geometric structure is observed:

(1) Type F is similar to local torch mode B; the geometric structure of the front resembles the shape of a trun�cated cone with the front boundary expanding with increasing distance from the point of introduction of sub�stance 1 (Fig. 20a).

(2) Type P is a planar reaction front that is a complete analog of mode A discussed above (Fig. 20b).

0.1

0.8

0.2 0.3 0.4 0.5

0.4

0.4

0.8

A

B

C

D

1 2 3 4

1 ' 2 '3 '

4 ' 5 ' 6 '7 '

8 ' 9 '

Fig. 19. The fields of temperatures and the concentrations of the monomer and the catalyst: Kp = 103 l mol–1 s–1, K0 = 1 s–1,

M0 = 1 mol l–1, = 10–2 mol l–1, DT = 1 m2 s–1, h = 0. Temperature T, K: (1) 310, (2) 312, (3) 320, and (4) 330. M0, mol l–1:

(1 ') 0.9, (2 ') 0.7, (3 ') 0.5, (4 ') 0.35, (5 ') 0.2, (6 ') 0.15, (7 ') 0.085, (8 ') 0.035, and (9 ') 0.016. A*, mol l–1: (D) 1 × 10–4, (A) 2 ×10⎯3, (B) 1 × 10–3, and (C) 5 10–4 [52].

0*A

Table 3. Dependence of the conversion rate, degree of polymerization ( ), and polydispersity ( ) on the radius ofthe reaction zone

R, M Conversion rate, wt % Zone

0.01 100 13 2.0 А

0.03 100 13 2.0

0.05 100 (97.7) 12 (30) 2.1 (3.1)

0.05 99.3 10 2.1

0.1 90.0 (90.0) 8 (21) 2.2 (3.7) Б

0.25 65.0 6 2.4

0.50 32.0 (29.7) 6 (17) 2.4 (4.0) В

Pn Pw/Pn

Pn Pw/Pn

82


DAVTYAN et al.

(3) Type D has no reaction front; the reaction occurs throughout the entire reactor volume, which is causedby strong reverse diffusion of the reagent flows with separated currents (Fig. 20c).

The formation of a certain type of reaction front depends on the ratio of V1/V2 rather than on their absolutevalues. The effect of V1/V2 on the front structure depending on the introduction method is presented in Table 4according to the data of [53–61].

According to the data of Table 4, reaction type F is implemented with the introduction of initial substance 1by method A(+l) and only at small ratios of V1/V2. On the contrary, reaction type D is formed at high ratios ofV1/V2, regardless of the method of reagent introduction. Planar front P appears as an intermediate state betweenreaction types F and D. From the point of view of the maximum yield of the goal product, planar front P is themost favorable, because only in this case can the uniform composition of the reaction flow along the radius ofthe reaction zone be ensured.

Besides the mentioned thermal modes, two more macroscopic types of frontal modes were observed, namely,“wave” (W, Fig. 20d) and “lace” (L, Fig. 20e) [51, 52, 58, 61].

Presented in Figs. 20d and 20e, the modes are probably unstable frontal modes, which appear as vibrationand spin modes.

It is interesting that such unstable modes were observed in the mixing of liquids of different viscosity and den�sity [51, 52, 58, 61].

Therefore, the occurrence of different modes of ultrarapid chemical reactions in turbulent flows indicatesthat the geometric shapes and dimensions of the reaction volume affect the yield and, in the case of polymeriza�tion, the molecular�weight characteristics of the resulting polymer. On the other hand, the possibility of mutualtransition from frontal modes of quasi�ideal displacement (A, P) to torch modes (B, W, F) and vice versa indi�cates the relation of the geometric dimensions of the reaction zones to the kinetic, hydrodynamic, and thermo�physical parameters of the process.

It should be noted that the problem of intensification of the process of convective heat transfer is of greatimportance for improving the characteristics of heat exchangers. Many different solutions have been proposed,with methods using the profiling of the channels of a heat exchanger taking precedence because of their relativesimplicity and technological feasibility [113, 114]. It was experimentally shown that the efficiency of the inten�sification of heat transfer of tubular channels with deep profiling can be significantly higher than that of shallow�profiled channels [62–64].

A new generation of energy� and resource�saving technology for the production of halogenated butyl rubberand other chlorinated rubbers with the use of tubular turbulent small�scale devices is described in [65–67].

Table 4. Geometric shape of the front in dependence on the supplement method and the feed rate of reagents

Method for supplying the reagent Type of reaction front

A (+l) 0.5–1.5 F

1.5–2.0 Mixed (F and P)

2.0–5.0 P

5.0–8.0 Mixed (P and D)

≥8.0 D

А (l = 0) ≤1.5 P

1.5–2.0 Mixed (P and D)

≥2.0 D

A (–l) 0.5–25 D

В (+l) 0.5–60 P

≥60 D

В (l = 0) 0.5–60 D

В (–l) 0.5–60 P

1

2

VV



Small�scale high�performance tubular turbulent devices of cylindrical structure were used in industry withexceptionally high efficiency in the implementation of the following processes:

(1) Synthesis of oligo�isobutylenes with molecular weight M = 600–6000, and obtaining of medium� (M =9000–40 000) and high� (M = 80 000–225 000) molecular polyisobutylenes and isobutylene copolymers with,for example, isoprene.

(2) Production of polybutenes.(3) Copolymerization of isobutylene with isoprene in the production of medium�molecular butyl rubber with

M = 25 000–60 000.(4) Sulfation of butylenes in the production of methylethylketone.(5) Chlorination of ethylene with molecular chlorine in a solution of dichloroethane.(6) Extraction of phenols in the washing of the absorption fraction of coal tar in coke production, etc.

Thus, investigations of the macrokinetic peculiarities of the cationic polymerization of isobutylene in turbu�lent flows were a research basis for the development of a new generation of resource�saving technologies usinghigh�performance small�scale reactors of original design. The studies performed for the first time on the small�scale tubular turbulent reactors allowed the improvement in the performance of the process by 4 to 100 times, anincrease in the yield and enhancement of the product quality (up to international standards and better), the pos�sibility of using different raw materials (up to 80–100% of the concentration of reagent), and a considerabledecrease in power consumption (20% or more). They significantly improved the sensitivity of the chemical pro�

(a)

(b)

(c)

(d)

(e)

Fig. 20. Typical fronts of the mixing of liquid flows: (a) torch (F), (b) planar (P), (c) drift (D), (d) wave (W), (e) lace (L) [55, 57].

84


DAVTYAN et al.

cess to catalytic poisons with a sharp decrease in reaction time (by 100–500 times or more), require considerablyless metal equipment, ensure higher ecological safety of the processes, and so on.

The macrokinetic regularities determined for the ultrarapid polymerization of isobutylene in tubular turbu�lent reactors and the use of new concepts enabled the development and organization of energy�saving, high�per�formance, and ecologically safe production of polyisobutylenes and polybutenes, (butadiene�styrene and stere�oregular) cis�1,4�isoprene synthetic rubbers, chlorinated and hydrochlorinated ethylene�1,2�dichlorethane,ethyl chloride, butylsulfuric acid in the production of methylethylketone, etc. It should also be noted that manyof the mentioned processes are deployed in the Commonwealth of Independent States (CIS) countries, not onlyin the Russian Federation.

8. PROBLEMS OF FRONTAL POLYMERIZATION

It should be noted that, besides the mentioned cases of wide implementation of frontal polymerization inindustry (various reactors with turbulent flows, a cylindrical reactor with radial symmetric laminar flows), frontalpolymerization is very promising in simpler and more affordable continuous and periodic reactors. Why, in spiteof the potential and obvious advantages of frontal polymerization as a new technological approach, are only theabovementioned reactors used in practice? Consideration of two real examples of frontal polymerization in peri�odic reactors can help answer the question.

It should be noted that, in the majority of published articles, the frontal polymerization process is performedin glass ampoules and under conditions of heat loss through the walls of the reaction vessel to the environment[1, 3, 7–9, 11–14, 18, 36–48, 76, 77, 91, 93, 99, 100, 102, 105, 106, 111, 112]. After the termination of frontalpolymerization, the reaction ampoules are cooled to room temperature at an arbitrary cooling rate.

It is obvious that frontal polymerization under conditions of heat loss—if it does not lead to the instability ofthermal autowaves with arising vibration and spin modes [93, 101–103, 115]—can rather considerably affect theproperties of the resulting polymer materials. Indeed, frontal polymerization performed in periodic reactorsunder conditions of nonuniform temperature distribution along the radius of the sample can affect the molecu�lar�weight characteristics, residual stress level, and monolithic structure of the resulting polymer materials. Inthis regard, it is interesting to consider the effect of the mentioned factors (heat loss, cooling of the reactionampoules after polymerization at an arbitrary rate) on the properties of polymer materials obtained by frontalpolymerization. To illustrate the idea, two typical examples of frontal polymerization are presented: the synthesisof (1) cross�linked three�dimensional thermoset material on the base of resorcinol diglycidyl ether [116] and (2)polycrystalline thermoset material, i.e., poly�ε�caprolactam [117].

8.1. Frontal Solidification of Resorcinol Diglycidyl Ether by 4,4�Diaminodiphenyl Sulfide

The frontal solidification of resorcinol diglycidyl ether (RDE) by 4,4�diaminodiphenyl sulfide (DAPS) wasperformed in glass ampoules 20 mm in inner diameter, using three different thermal modes [116]:

(1) With full thermal insulation of the reaction ampoules both in the process of frontal solidification and afterits termination;

(2) Under condition of heat loss to the environment both in the process and after the termination of frontalpolymerization;

(3) Under condition of thermal insulation during frontal polymerization and with cooling of the samples atan arbitrary rate after the termination of frontal polymerization.

The temperature profiles of the frontal solidification of RDE by DAPS, obtained with full thermal insulationof the reaction ampoules (curve 1) and with heat transfer to the environment (curve 2), are presented in Fig. 21.As seen from the figure, until the limiting values of the thermal waves are attained, the temperature profilesalmost coincide with each other. The front velocity, determined by the readings of two thermocouples situatedat different distances from the beginning of the reactor, is 2 cm/min.

Heat loss affects the temperature profiles only after the termination of the solidification process, which canbe explained by the location of the thermocouples in the central part of the solidified samples [116]. In fact, thedetermination of the radial temperature distribution showed that the temperature profiles were identical in thecentral part and rather different in the peripheral regions of the samples (Fig. 22).

The values of tensile strength (σ), modulus of elasticity (E), and elongation (ε), which are the averaged mea�surements of three samples [116], are presented in Table 5. According to the data of [116], all samples were ther�mally treated in a muffle furnace at 180°С for 2 h; then they were slowly cooled to room temperature.

Comparative analysis of the data of Table 5 shows that, at the stage of the formation of three�dimensionalpolymer networks in nonuniform temperature fields (Fig. 22, curve 1), internal stress accumulates, which can�not be principally relaxed by the thermal treatment of the samples. The point is that, because of the topological



defects that are formed in the polymer grid during the solidification process, the noted stress leads to the forma�tion of additional load in some fragments of the three�dimensional polymer. Therefore, the values of σ, E, andε for the sample obtained in the presence of heat loss from the reaction zone to the environment (experiment 2)are approximately 30% lower than for the samples obtained under thermal insulation (experiment 1) or aftercooling at an arbitrary rate (experiment 3). The residual stress arising after cooling at an arbitrary rate, as

explained in [116], is completely relaxed upon thethermal treatment of the samples at 180°С.

8.2. Frontal Polymerization of ε�Caprolactam

The temperature profiles of the anionic frontalpolymerization of ε�caprolactam, obtained in [117],are presented in Fig. 23.

It follows from curves 1–3 (Fig. 23) that, after thetermination of frontal polymerization, the adiabaticheating of the reaction mixture is 170°С. According to

50

Time, t0

100

150

200

1 2

T, °C

Fig. 21. Temperature profiles of the frontal solidification of RDE by DAPS in (1) the presence and (2) absence of heat loss [116].

0.2

100

050

0.4 0.6 0.8 1.0 r, mmm

1

2150

200

T, °C

Fig. 22. Limiting heating temperatures as a function of the sample radius in the (1) absence and (2) presence of heat loss [116].

Table 5. Physicomechanical characteristics of the samplesof epoxy compounds synthesized under thermal conditionsof 1, 2, and 3 (see ch. 8.1)

No. σ, MPa E × 10–4, MPa ε, %

1 160/170 40/38 3/3

2 110/120 23/30 2/2.3

3 165/170 40/42 3.3/3

86


DAVTYAN et al.

the data of [118], the degree of crystallinity of the resulting poly�ε�caprolactam at 170°С is ~0.48. It should alsobe noted that a uniform distribution of the limiting temperature of thermal waves is observed along the radialdirection [117], which indicates the adiabatic character of the propagation of the polymerization–crystallizationfront. The front velocity, determined by thermocouple readings, is 0.36 cm min–1.

To study the effect of thermal cooling modes on the monolithicity of the samples, several samples of poly�ε�caprolactam were synthesized under identical conditions of frontal polymerization [117].

To find the thermal cooling modes enabling uniform temperature distribution and degree of crystallinity overthe sample radius, a thermal problem of optimal regulation was solved by numerical methods with the use of afour�point implicit system [117]. For this purpose, it was assumed that at r = 0 the adiabaticity condition is ful�filled on the axis of symmetry, while at the boundary r1 the contact between the polymer and the reactor walls isideal. It was also assumed that at the external boundary of the reactor wall, that is, at r = r2, the heat transfer

occurs according to Newton’s law, namely, . Here, λ1 is the heat capacity, T is temper�

ature, F is a heat transfer coefficient, and s and ν are the surface and volume of the reactor; the temperature ofthe reactor side surface ( ) is the parameter to be regulated. It was also supposed that, at the initial time, thetemperatures of the polymer mixture and the reactor walls are the same over the entire length of the reactor, andthe polymer is molten.

Therefore, with the mentioned approximations, the equations of heat transfer and crystallization with thecorresponding initial and limiting conditions were solved by numerical methods [117]. The regulation of thecooling process of molten poly�ε�caprolactam supposes the determination of a law of the change of function

that enables the uniform distribution of both temperature and degree of crystallinity along the reactorradius during the entire process. Otherwise, if the sample is molten, the crystallization initiating at the reactorwalls can propagate along the radial direction and, because of crystallization shrinkage, a void can occur in thecenter of the sample, which can disturb the continuity of the medium. It should also be noted that, if in the tem�perature range from Та to the glass�transition temperature Тg, the minimization of temperature–crystallizationinhomogeneities is the main requirement. At temperatures lower than Тg, the counting of the times of relaxationof residual stress arising because of crystallization and thermal shrinkage also becomes an important factor inregulation. Counting of the times of residual stress relaxation supposes the solving of the equations of heat trans�fer and crystallization kinetics simultaneously with the equations of the deformation of viscous�elastic mediawith the properties of the cooled and crystallized material, changing in time. However, note that such problemswere not considered in [117]. Therefore, in the regulation law the relaxation times are counted indirectly, just asit is done in the thermal treatment of samples of cross�linked three�dimensional polymers, e.g., those obtainedby the solidification of polyester acrylates [119] or epoxydiane oligomers [27].

[ ]Tr2

1 1( )r r

T sh T tr =

∂λ = −

∂ ν

( )1rT t

( )1rT t

2

120

080

4 6 t, min

100

160

140

180

T, °C

1 2 3

Fig. 23. Temperature profiles of the anionic frontal polymerization of ε�caprolactam. The concentrations of the catalyst and theactivator, 0.05 mol/l [117].



In the opinion of the authors of [117], function can be considered an acceptable regulation at the sampleboundary, if the solution meets the following limitations:

The time of the cooling process tk is considered attained if , where Тu is the temperature of oper�ations of the resulting sample, e.g., room temperature.

In these inequalities, а1 and а2 are the preset values (а1 = ~1°С, а2 = ~2%) determining the acceptable dropin temperature and degree of crystallinity during the cooling process. Here, in the class of acceptable functions

, one needs to find the function enabling the minimum value of tk.As a result of numerous computational experiments regarding the mentioned limitations, a dependence of

was found, presented in Fig. 24.Figure 25 demonstrates the space–time distribution of temperature (Fig. 25a) and degree of crystallinity

(Fig. 25b) over the reactor radius for the regulated cooling mode.It can be seen from Fig. 25 that, indeed, at some stages of cooling the requirements expressed by the inequal�

ities are violated. It is shown on the basis of numerical computation that the process can be regulated more effec�tively if, at the initial stages of cooling, the following conditions are fulfilled: and

– ; that is, in the central part of the reactor, the temperature is lower (Fig. 25a, curve 2)and the degree of crystallinity is higher (Fig. 25b, curve 2) than at the reactor walls. Otherwise, the governabilitybecomes worse and the cooling time tk considerably increases.

Under conditions of frontal polymerization, several samples of poly�ε�caprolactam were obtained at the ini�tial temperature of 85°С [117]. A cross�section of one of the samples showed that, in the central part, a loosercrystalline structure was visually observed, which is difficult to note in the images. Therefore, to conserve theeffect of the cooling process on the monolithicity of semicrystalline polymers obtained by frontal polymeriza�tion, the temperature of all samples was uniformly increased to 225°С, which corresponded to the molten stateof poly�ε�caprolactam. Then, several experiments were performed including cooling both at an arbitrary ratethrough the reactor side surface and in the thermal mode close to that calculated for optimal cooling (Fig. 26)[117].

It should be noted that all samples after cooling were apparently the same (Fig. 26a). To determine theirmonolithicity, the synthesized samples were cut. Photographs of the cross�sections are presented in Fig. 26b. Itis seen that the sample of poly�ε�caprolactam obtained by cooling at an arbitrary rate has a defect as a void spacelocated in the center of the sample, while the sample obtained in the optimal cooling mode is monolithic, with�out macro� or microvoids (Fig. 26b). Thus, the frontal polymerization of ε�caprolactam followed by cooling atan optimal thermal mode yields large�scale, defectless, and monolithic samples of poly�ε�caprolactam. It isobvious that other approaches can in principle be used to find the cooling modes ensuring the monolithicity anddefectlessness of samples synthesized in the frontal or other high�temperature thermal modes of polymerization.For example, by the readings of two thermocouples (situated in the center and periphery of the reactor) entering

( )1rT t

( ) ( ) ( )

( ) ( ) ( )

1 1

2 2

max , min ,

max , min , .rr

rr

h t T r t T r t a

h t r t r t a

= − <

= β − β <

( ) u, kT r t T=

( )1rT t

( )1rT t

( ) ( )10, , 0T r t T r r t−

= − = =

( )0,r tβ = ( )1 , 0r r t−

β = >

3

100

0 6 9 12 Time, h

50

200

150

Tr2, °C

Fig. 24. Optimal cooling mode of molten poly�ε�caprolactam in the cylindrical reactor, 0.15 m in height and 0.1 m in diameter[117].

88


DAVTYAN et al.

the computer database, one can require that the above inequalities be fulfilled during the entire process of samplecooling. Such regulation of the cooling process also results in the monolithicity of samples (Fig. 26d); however,a significantly longer time is needed in this case.

9. CONCLUSIONS

Thus, in the present review, we tried to analyze the current literature and our own data on frontal polymer�ization. Our objective was to show not only the advantages of this nonconventional method of polymerizationbut also the problems challenging researchers and engineers in its technological implementation. The techno�logical modes of frontal polymerization performed by Russian researchers under continuous conditions are ana�lyzed. The main advantages of frontal polymerization are summarized, such as the simplicity of technologicalimplementation; high performance; ecological safety; and wide possibilities in the synthesis of various polymers,copolymers, polymer hydrogels, gradient materials, polymer nanocomposites, and large�scale composite prod�ucts.

At the same time, the problems related to the specificity of frontal polymerization modes are analyzed, thatis, low yields of the product of initiated polymerization and poor molecular�weight characteristics. Recommen�

1

50

0 2 3 4 5r, cm

100

150

200

(а)

1

0.2

0 2 3 4 5r, cm

0.3

0.4

0.5

(b)T, °C

1

2

3

4

5

6

7

8

9

0.6

0.1

β

8, 97654

3

2

1

Fig. 25. The space–time distribution of (a) temperature and (b) degree of crystallinity over the reactor radius. Initial temperature,225°C; time, h: (1) 0.5, (2) 1.7, (3) 2.3, (4) 3.0, (5) 4.7, (6) 6.3, (7) 6.9, (8) 7.5, and (9) 13.0 [117].

(а) (b) (c) (d)

Fig. 26. Samples of poly�ε�caprolactam obtained at different cooling modes. (a) External appearance and (b–d) the cross�sec�tions of samples: (b) cooling at an arbitrary rate, (c) cooling under calculated optimal conditions, and (d) cooling under optimalconditions controlled by thermocouples [117].



dations are given for not only increasing the yield but also improving the MWD characteristics. It should be spe�cially noted that, if the problems on the regulation of the polymer yield and MWD characteristics were discussedearlier in different publications, the issues related to heat transfer from the reaction zone to the environment andthe effect of cooling on the properties of the samples obtained in the frontal mode are reviewed for the first time.Recommendations are given for determining the necessary conditions for the synthesis of polymer materials orcomposites with predetermined properties. The conditions for the regulated cooling mode of polymer semicrys�talline thermoset materials are determined, ensuring the defectlessness of the products.

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