Article pubs.acs.org/Macromolecules
Experimental and Modeling Study of Acrylamide Copolymerization with Quaternary Ammonium Salt in Aqueous Solution Danilo Cuccato, Giuseppe Storti,* and Massimo Morbidelli Institute for Chemical and Bioengineering, ETH Zurich, Vladimir-Prelog-Weg 1, 8093 Zurich, Switzerland ABSTRACT: The free-radical copolymerization of acrylamide with the cationic monomer DMAEA-Q in aqueous medium is investigated with special attention to its composition behavior, which reveals to be affected by the electrostatic interactions between the charges in the system. The reaction kinetics is determined by in situ 1H NMR experiments, showing a peculiar dependence of the copolymer composition upon initial monomer and electrolyte concentrations. A kinetic model simulating the evolution of copolymer composition as a function of conversion is developed, accounting for the nonconventional features of the system. Namely, a description of the electrostatic interactions based on the DLVO theory is introduced to define a functional dependence of the rate coefficients on the ionic strength. Secondary reactions are also included due to the acrylic nature of both monomers. The proposed model is applied to estimate the corresponding reactivity ratios and proves to exhibit the correct functionality with respect to monomer concentration and ionic strength.
■
INTRODUCTION Polyelectrolytes are nowadays largely used in a wide range of applications, primarily those aimed at modifying the stability of aqueous solutions.1,2 Some interesting properties of polyelectrolytes come from the presence of ionizable side-chain groups attached to the polymer backbone: within a polar solvent, such groups can experience different extents of dissociation, thus releasing counterions and making the polymer chain a polyvalent macroion. The strength of a polyelectrolyte is determined by its degree of dissociation in solution: this property is affected by the nature of the charged moieties and the extent of counterion condensation, which is in turn a function of the charge density of the macroion.3 The resulting charged macromolecules are subject to electrostatic inter- and intramolecular interactions, and such interactions explain the peculiar behavior of polyelectrolytes in solution.4 As a matter of fact, the mutual correlation between some fundamental solution properties of polyelectrolytes, such as intrinsic viscosity, ionic strength, solution conductivity, molecular weight, and polymer chain conformation, is not yet clearly understood or easily predicted.5−8 Cationic polymers, also referred to as polycations, are polyelectrolytes leaving macrocations after dissociation. They are mainly used as flocculants in wastewater treatment and paper-making industry, in the stabilization−destabilization of emulsions, and in the production of cosmetics and pharmaceuticals.6,9 Latest applications of these materials are found in the biochemical and medical fields, such as the manufacture of implant coatings and controlled drug delivery devices.10 Indeed, nanoparticles made of polycations can be effectively used to package genetic material (e.g., siRNA) in © XXXX American Chemical Society
order to bypass degradative bioenvironments and achieve targeted release.11 Cationic polymers are synthesized by homopolymerization of cationic monomers or, more preferably, by copolymerization of these compounds with other neutral monomers, primarily acrylamide (AAm). The latter route has the advantage of producing higher molecular weights, as the molar masses are limited by the electrostatic hindrance of the propagation reaction in the case of homopolymerization.12−14 The most important categories of cationic monomers used to synthesize cationic polymers include ammonium, sulfonium, and phosphonium salts. The former ones are the most attractive in terms of monomer stability and final molecular weights.15 Among ammonium salts, the quaternary ones, also referred to as quats, are characterized by the presence of permanent positive charges: the corresponding counterions are dissociated at any pH value of the solution. They find applications in surface treatment, particularly in the biomedical field due to their antimicrobial properties.16 The cationic monomers 2(acryloyloxyethyl)trimethylammonium chloride (DMAEA-Q), 2-(methacryloyloxyethyl)-trimethylammonium chloride (DMAEM-Q), diallyldimethylammonium chloride (DADMAC), and the double charged bis-1,3(trimethylamino)-2propyl methacrylate dichloride (di-M) are popular examples of quats: they differentiate themselves in chemical structure, linear charge density, and reactivity in the context of radical polymerization.13,17,18 Received: May 28, 2015 Revised: July 15, 2015
A
DOI: 10.1021/acs.macromol.5b01148 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
and electrolyte concentration on the different reactivity ratios are proposed.
Quaternary ammonium salts for the synthesis of polycations have been subject of several studies, some of which focused on the kinetics of copolymerization between quats and other cationic or neutral monomers. In particular, special attention has been devoted to the characterization of the evolution of copolymer composition of polyelectrolytes as well as of the polymer properties (e.g., conductivity, molar mass, intrinsic viscosity) during the polymerization reaction. Mayo−Lewis plots and reactivity ratios have been obtained experimentally for various relevant copolymers involving quats: AAm-co(DMAEA-Q),6,8,12,14,17,19−22 AAm-co-(DMAEMQ),12,14,17,19,22 AAm-co-DADMAC,12,14,17 (di-M)-co-AAm, and (di-M)-co-(DMAEA-Q).13 Recent studies on the copolymerization between AAm and acrylic acid (AA) in water, with AA in the fully ionized form of sodium acrylate, have revealed that its kinetic behavior is affected by the ionic strength of the solution. Namely, the estimation of reactivity ratios appears to be affected by some factors (e.g., solvent polarity, pH, presence of added salts) determining concentration and nature of the charged species in the system.23 The same feature was observed also in copolymer systems involving AAm and other charged monomers.24 Other investigations on the homopolymerization of ionizable monomers revealed a dependence of the propagation kinetics on the degree of ionization and on the addition of counterions. The former dependence was attributed to increased hindrance of the transition state structure at increasing monomer ionization; the latter has been explained by a mechanism of formation of triple ions and ion pairs.25,26 The interference of the amount of charges in the system with the reactivity of ionic monomers can be also explained with the concept of electrostatic screening.18,27 During the polymerization of a charged species, the electrostatic repulsion between the charged moieties of growing radical and approaching monomer represents a hindrance to the propagation reaction. If an electrolyte is added to the system, these interactions are shielded by the presence of counterions in solution: such screening of the electrostatic forces is a function of the concentration and type of charges in the systems, which can be quantified by the ionic strength. Of course, ionic monomers behave like electrolytes in solution, and thus their concentration contributes to build up the ionic strength. In this work, the copolymerization of the quaternary ammonium salt DMAEA-Q with AAm in aqueous solution is examined. DMAEA-Q is chosen due to its relevance among the permanently charged cationic monomers. The system is first investigated experimentally with the aim of characterizing reaction kinetics and evolution of copolymer composition. Few works about the investigation of the copolymerization of this cationic monomer with AAm can be found in the literature.6,8,12,14,17,19−22 As an improvement to the previous studies, the effect of reaction parameters such as initial monomer concentration and composition is thoroughly investigated in this work, specifically extending the analysis from very low to highly concentrated solutions, in order to shed light on the composition behavior. A state-of-the-art technique based on 1H NMR spectroscopy is adopted to collect very accurate data of monomer conversion and composition as a function of time. In a second part, a model of copolymer composition as a function of conversion accounting for the electrostatic nature of the system is developed and validated by comparison with the experimental results. Finally, effective relationships accounting for the impact of charged monomer
■
MATERIALS AND METHODS
Copolymerization reactions are carried out in deuterium oxide (D2O, Cambridge Isotope Laboratories, 99% purity) and using NMR tubes (5 mm NMR tube, type 5UP, 178 mm, ARMAR Chemicals) as reactors, which are inserted in an operating NMR spectrometer (Bruker UltraShield 500 MHz/54 mm magnet system). For each experiment, a solution of the two monomers AAm (Sigma-Aldrich, 99% purity) and DMAEA-Q (provided by BASF, 80% mixture in water with 60−70 ppm of MEHQ inhibitor) in D2O is prepared beforehand: the radical initiator 2,2′-azobis(2-methylpropionamidine) dihydrochloride (V-50, Acros Organics, 98% purity) is added, and about 0.6 mL of the reacting mixture is injected into the NMR tube, which is stored at 0 °C. The total monomer concentration in the initial solution w0M (weight fraction, %) is ranging from 1% to 20%, with initial composition f0A (mole fraction of AAm) spanning from 0.1 to 0.9, while the initial concentration of V-50 is kept constant at 3 × 10−3 mol L−1 for all the reactions. The polymerization is initiated by thermal activation of the initiator as soon as the NMR tube containing the reacting solution is inserted into the NMR spectrometer, previously heated up to the set point temperature (Tset). All of the reactions are carried out at Tset equal to 50 °C. Total monomer conversion (χ, molar conversion) and residual monomer composition (fA, mole fraction of AAm) are measured as a function of the polymerization time by a series of 1H NMR acquisitions. In Situ 1H NMR Technique.28 In situ values of composition of the residual monomer mixture, fA, and conversion, χ, have been monitored online with accuracy by 1H NMR, even in the case of very fast kinetics. The reaction characterization was carried out by acquiring single 1H NMR spectra, also referred to as 1D slices, all along the polymerization reaction: each spectrum at time tn actually represents the average properties of the system from tn−1 to tn, the time interval during which scans are continuously collected. The values of fA and χ have been evaluated based on the areas of the hydrogen peaks corresponding to monomer and polymer (cf. Figure 1) using the following equations:
fA =
χ=
AreaA AreaA + AreaB AreaP AreaP + AreaA + AreaB
(1)
(2)
where A is AAm, B the ionic monomer DMAEA-Q, and P the produced polymer. As an example, the series of 1H NMR spectra taken at selected times for a typical copolymerization reaction AAm-DMAEA-Q is shown in Figure 2. The 1D slices acquired by in situ 1H NMR all along the reaction are combined in the so-called 2D spectrum, where the second dimension corresponds to the polymerization time. From the automatic processing of such 2D spectrum, the time evolution of the key-peak areas (i.e., time decrease in the monomer peak areas and time increase in the polymer peak one) is extracted. At the same time, the actual starting point of the polymerization and information about possible temperature drifts with respect to Tset are recorded, as shown in Figure 3. Temperature Control. One critical feature related to the use of in situ 1H NMR is represented by the temperature control, which can be an issue in the case of exothermal reactions. In our equipment the temperature is controlled by air flow on the probe: in the case of high monomer concentration, such heat removal may not be adequate and some relevant temperature increase above Tset can take place. On the other hand, the drift in reaction temperature from Tset can be roughly estimated from the drift in chemical shift of some reference peaks during the reaction. Namely, the quality of the temperature control can be monitored by observing the recorded 2D spectrum, as highlighted B
DOI: 10.1021/acs.macromol.5b01148 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
by 1H NMR at different temperatures in the range 50−70 °C. For each selected temperature value, the corresponding drift in chemical shift of one monomer peak referred to its chemical shift at 50 °C (ΔS) was measured. The resulting correlation between temperature drift (ΔT, referred to Tset = 50 °C) and drift in chemical shift is shown by the inset in Figure 4. Although the estimated temperature increase resulted to be systematically larger at larger values of w0M and f0A, it should be noted that the temperature drifts measured for all the investigated reactions were always smaller than 2 °C thanks to sufficiently large air flow to the probe.
■
Figure 1. 1H NMR spectrum of the copolymerization of AAm with DMAEA-Q at 50 °C (run 4 in Table 1) at a specific reaction time (corresponding to χ = 79%). The assignments of the hydrogen peaks of residual monomers (A = acrylamide, B = DMAEA-Q) and produced polymer (P) are provided.
Figure 2. Series of 1H NMR spectra of the copolymerization of AAm with DMAEA-Q at 50 °C (run 4 in Table 1) at increasing reaction times: for each spectrum, the corresponding value of monomer conversion is indicated. in Figure 4 for the case of a copolymerization reaction with significant temperature increase. The drift in chemical shift (ΔS, ppm) of the monomer peaks can be brought back to the corresponding temperature drift (ΔT) by using the approximate equation
ΔT = Tmax − Tset ≈ ΔS· 100
EXPERIMENTAL RESULTS
Copolymerization reactions between AAm and DMAEA-Q have been carried out first at the larger w0M values of the examined experimental range (i.e., 10% and 20%) and varying the initial monomer composition in terms of AAm molarity from 0.1 to 0.9. Details on the experimental conditions adopted are reported in Table 1 (cf. runs 1−12). From the experimental results shown in Figure 5 it can be readily observed that the composition behavior of the system depends on the initial monomer concentration. The effect on the composition curves is notable at any value of initial composition. In the specific case at f0A = 0.5, the behavior of the two curves reveals how the azeotropic composition changes accordingly (i.e., the azeotropic composition in terms of f0A is above 0.5 with w0M = 10% and below 0.5 with w0M = 20%). A second series of experiments have been carried out at a welldefined value of initial monomer composition ( f0A = 0.5) and varying the initial monomer concentration from 1% to 20%, in order to investigate more carefully the monomer concentration effect on the composition behavior of the system. Details on the experimental conditions adopted are reported in Table 1 (cf. runs 13−15, 4, and 10). The results reported in Figure 6 show that the composition behavior of the system is strongly affected by the initial amount of monomer in a wide range of values of monomer concentration. It is apparent that these data of composition cannot be simulated by using a conventional terminal model of binary copolymerization which involves constant reactivity ratios, but they must rather exhibit nonnegligible composition dependence. Electrostatic Effect. With the aim of understanding the mechanisms responsible of the observed composition behavior as a function of the initial monomer concentration, let us consider the properties in solution of DMAEA-Q, which is positively charged due to the complete dissociation of its counterion (chloride ion). The ionic nature of DMAEA-Q is likely to affect its mobility within an electrolyte (i.e., aqueous solution containing DMAEA-Q cations and chloride anions), which can in turn affect its diffusion toward other charged species. This phenomenon becomes relevant when a DMAEA-Q monomer molecule reacts with a DMAEA-Q radical unit (i.e., an active chain with radical terminal unit of DMAEA-Q), as in the case of propagation. Specifically, the diffusion of monomer molecules toward the radical is going to be affected by the electrostatic (repulsive) interaction between the corresponding charged groups. On the other hand, the ionic strength of the system representative of a certain electrolyte concentration defines the extent of the electrostatic screening of the forces between the approaching charged groups in the case of propagation, as already anticipated in the Introduction.13,18 Focusing on a binary copolymer system where one monomer is charged while the other is not and considering a terminal model of copolymerization, among the four possible propagation pathways only the kinetics of the reaction involving a charged monomer and a charged radical is likely to be affected by the ionic strength. Consequently, the reactivity ratios defining the relative extent of the propagation rates are also functions of the ionic strength. Under the long-chain approximation (LCA) the composition behavior of a copolymer system is determined essentially by the reactivity ratios; thus, it is likely to be influenced by the ionic strength as well. To verify this expectation, copolymerization reactions have been carried out following the same recipes adopted for some of the previously mentioned experiments, with the addition of well-defined
(3)
Equation 3 has been validated empirically. Namely, a sample containing DMAEA-Q and AAm monomers only has been analyzed C
DOI: 10.1021/acs.macromol.5b01148 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
Figure 3. 1H NMR 2D spectrum for the copolymerization of AAm with DMAEA-Q at 50 °C (run 11 in Table 1). The assignments of the hydrogen peaks (cf. Figure 1) are provided together with information about temperature drift and reaction starting time.
Figure 4. Drift in chemical shift (ΔS) of one monomer peak due to the temperature increase by reaction visualized on the 2D spectrum taken by in situ 1H NMR. Inset: empirical calibration chemical shift vs temperature.
Table 1. Experimental Recipes for the Copolymerization Reactions of AAm with DMAEA-Q at 50 °C run
w0M (%)
f0A
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
10 10 10 10 10 10 20 20 20 20 20 20 1.0 2.5 5.0 1.0 2.5 5.0 10
0.10 0.30 0.41 0.50 0.71 0.89 0.20 0.30 0.40 0.49 0.70 0.78 0.48 0.49 0.52 0.49 0.49 0.49 0.50
w0S (%)
Ce (mol kg−1)
5.0 4.6 3.9 2.6
0.55 0.50 0.46 0.42 0.30 0.15 1.19 1.11 1.04 0.95 0.70 0.56 0.04 0.10 0.20 0.95 0.95 0.95 0.95
Figure 5. Experimental results of residual monomer mixture composition as a function of conversion for the copolymerization reactions of AAm with DMAEA-Q at 50 °C corresponding to runs 1− 12 in Table 1. Initial monomer content: w0M = 10% (triangles) and 20% (circles). behavior. In particular, if the initial ionic strength of experiments carried out at different monomer concentration is adjusted to the same value, these experiments exhibit a similar composition drift. In Figure 7, the initial ionic strength of runs 13−15 and 4 has been increased to 0.95 mol kg−1 (i.e., the ionic strength of the experiment at w0M = 20%, run 10) by addition of amounts of salt whose weight fractions, w0S, are detailed in Table 1. It should be pointed out that all the values of final
amounts of salt (NaCl) to change the initial ionic strength without modifying the monomer concentration. Details on the experimental conditions adopted are reported in Table 1 (cf. runs 16−19 and 10). The results in Figure 7 compared with those in Figure 6 show that increasing the ionic strength in the system changes the composition D
DOI: 10.1021/acs.macromol.5b01148 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
formation due to backbiting and consumption due to MCR propagation) the fraction of MCRs is inversely proportional to the monomer concentration, as shown by eq 4:30,31
kbb Q ≅ T R kp M 0(1 − χ )
(4)
where Q is the concentration of MCRs, R the concentration of secondary radicals, kbb the backbiting rate coefficient, kpT the propagation rate coefficient of MCRs, and M0 the initial monomer concentration. Since the two types of radicals are generally characterized by different propagation rate coefficients (i.e., kTp is some orders of magnitude smaller than the corresponding rate coefficient of secondary radicals, kp),32−35 the rate of monomer conversion at a given monomer conversion is affected by a change in the initial monomer concentration. More precisely, an increase in the initial monomer concentration results in an increase in the polymerization rate due to an increase of R with respect to Q, according to eq 5.
Figure 6. Experimental results of residual monomer mixture composition as a function of conversion for the copolymerization reactions of AAm with DMAEA-Q at 50 °C corresponding to the runs 13−15, 4, and 10 in Table 1. The initial monomer content of each experiment is detailed in the picture.
dχ = (1 − χ )(kpR + kpTQ ) dt
(5)
Considering a copolymer system, it is easy to show that the rate of copolymerization exhibits the same dependence on the relative amount of the two radicals and thus on the variation in the initial amount of monomer. However, the way how the copolymer composition behavior depends on the initial monomer concentration due to the effect of secondary reactions is not much easier to be predicted. With the aim of understanding if the two features proposed (i.e., electrostatic effect and secondary reactions) are adequate to explain the peculiar composition behavior function of initial monomer concentration and ionic strength observed experimentally, a comprehensive model of copolymer composition is developed.
■
MODEL OF COPOLYMER COMPOSITION Assuming a terminal model of copolymerization (i.e., the reactivity of an active chain is determined only by the nature of its radical unit), the time evolution of chain composition in a binary copolymer system with monomers A and B is described by four propagation reactions: kp , AA
Figure 7. Experimental results of residual monomer mixture composition as a function of conversion for the copolymerization reactions of AAm with DMAEA-Q at 50 °C corresponding to runs 16−19 and 10 in Table 1 (the initial ionic strength has been adjusted to the value of 0.95 mol kg−1 by addition of NaCl). The initial monomer content of each experiment is detailed in the picture.
RA + MA ⎯⎯⎯→ RA kp , BB
R B + MB ⎯⎯⎯→ R B kp , AB
RA + MB ⎯⎯⎯→ R B kp , BA
R B + MA ⎯⎯⎯→ RA
monomer composition in Figure 7 are between 0.48 and 0.55, while the corresponding range in Figure 6 is by far larger (between 0.10 and 0.55). Please note that the scale of composition values on the y-axis of Figure 7 goes from 0.45 to 0.55. This result confirms that the monomer concentration dependence of the composition behavior can be explained mainly in terms of a dependence on the ionic strength. However, the results in Figure 7 show that the electrostatic effect is not the only contribution determining the peculiar composition behavior of the system. Namely, an effect on the composition behavior of the initial monomer concentration which cannot be attributed to the ionic strength is observed, and it is responsible for the slight difference between the reported curves. In particular, the data in the high-conversion region reveal that such additional composition dependence is proportional to the monomer concentration. Secondary Reactions. These reactions, which are well-known to be relevant in acrylate systems, can be responsible for a monomer concentration dependence of the kinetic behavior in radical polymerization.29 Studies on this effect on polymerization kinetics, particularly backbiting and propagation of midchain radicals (MCRs), revealed that in steady-state conditions (i.e., at the equilibrium between MCR
(6)
where RA and RB are active chains with radical of type A and B, respectively, and kp,ij is the propagation rate coefficient of the reaction between radical Ri and monomer Mj. For this basic kinetic scheme, the instantaneous copolymer composition is readily evaluated through the well-known Mayo−Lewis equation. This equation can be implemented in the Skeist formula to obtain a function of the residual monomer composition with respect to the monomer conversion that exhibits an explicit dependence on the reactivity ratios (rA and rB):36,37 df A dχ
rAfA 2 + fA fB 2
=
rAfA + 2fA fB + rBfB2
χ−1
− fA (7)
where f B = 1 − fA. The reactivity ratios are defined as a function of the four propagation rate coefficients introduced in the kinetic scheme reported above (cf. eq 6): E
DOI: 10.1021/acs.macromol.5b01148 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules rA =
rB =
kp , AA kp , AB
balance equations of the four radical species, under the assumption of quasi-steady-state (QSSA), can be written as follows:
(8)
kp , BB
−kp , ABRAMB + kp , BARBMA − kbb , AAFARA − kbb , ABFBRA
kp , BA
(9)
+ kpT, AAQ AMA + kpT, BAQ BMA = 0
Secondary Reactions. Equation 7 needs to be modified if secondary reactions such as backbiting and MCR propagation are included in the kinetic scheme. Four backbiting reactions are required to describe the radical shift from the two existing types of chain-end radicals to any possible unit inside the growing chain, thus forming a specific type of MCR:
(12)
−kp , BARBMA + kp , ABRAMB − kbb , BBFBRB − kbb , BAFARB + kpT, BBQ BMB + kpT, ABQ AMB = 0
(13)
kbb , AAFARA + kbb , BAFARB − kpT, AAQ AMA − kpT, ABQ AMB = 0
kbb , AA
RA ⎯⎯⎯⎯→ Q A
(14)
kbb , BB
kbb , BBFBRB + kbb , ABFBRA − kpT, BBQ BMB − kpT, BAQ BMA = 0
R B ⎯⎯⎯⎯→ Q B
(15)
kbb , AB
RA ⎯⎯⎯⎯→ Q B
where FA and FB are the instantaneous copolymer compositions. These compositions were used because, at given polymerization time and type of terminal radical, the probability of backbiting to a midchain unit of type i is proportional to the probability of finding a unit of the same type inside the active chains, which is no other than the corresponding instantaneous copolymer composition. The time evolution of monomer concentration must consider the MCR propagation contribution, leading to the following monomer balance equations:
kbb , BA
R B ⎯⎯⎯⎯→ Q A
(10)
where QA and QB are active chains with a midchain radical unit of type A and B, respectively, and kbb,ij is the backbiting rate coefficient of the radical shift from the terminal unit of an active chain Ri to an intrachain unit of type j in the same chain. Given that MCRs are produced, their propagation kinetics is also considered: kpT, AA
Q A + MA ⎯⎯⎯→ RA
dMA = −kp , AARAMA − kp , BARBMA − kpT, AAQ AMA dt
kpT, BB
Q B + MB ⎯⎯⎯→ R B
− kpT, BAQ BMA
(16)
kpT, AB
Q A + MB ⎯⎯⎯→ R B
dMB = −kp , BBRBMB − kp , ABRAMB − kpT, BBQ BMB dt
kpT, BA
Q B + MA ⎯⎯⎯→ RA
(11)
− kpT, ABQ AMB
kTp,ij
where is the propagation rate coefficient of the reaction between midchain radical Qi and monomer Mj. The mass FA =
From eqs 16 and 17, FA is readily expressed as follows:
kp , AARAMA + kp , BARBMA + kpT, AAQ AMA + kpT, BAQ BMA dMA = dM MA(kp , AARA + kp , BARB + kpT, AAQ A + kpT, BAQ B) + MB(kp , BBRB + kp , ABRA + kpT, BBQ B + kpT, ABQ A)
where M = MA + MB. Unfortunately, eq 18 cannot be reduced to a compact form like the Mayo−Lewis formula where the radical concentrations are no more involved. Consequently, when secondary reactions are considered, the Skeist formula df A dχ
=
(17)
becomes slightly more complicated (eq 19), to be integrated together with three out of the four algebraic eqs 12−15, the stoichiometric relationship (RA + RB + QA + QB = Rtot), and eq 18 for FA.
fA (1 − fA )
kp , AARA + kp , BARB + kpT, AAQ A + kpT, BAQ B − kp , BBRB − kp , ABRA − kpT, BBQ B − kpT, ABQ A
χ−1
fA (kp , AARA + kp , BARB + kpT, AAQ A + kpT, BAQ B) + fB (kp , BBRB + kp , ABRA + kpT, BBQ B + kpT, ABQ A)
For a given set of rate coefficient values, the previous system of equations describes the composition behavior as a function of the initial monomer concentration. Note that the monomer concentrations appearing in eqs 12−15 are readily evaluated as a function of conversion and monomer composition ( f i) as follows: Mi = Mfi = M 0(1 − χ )fi
(18)
(19)
where the dependence on the initial monomer concentration (M0) is revealed. Electrostatic Effect. The electrostatic effect is accounted for by introducing a dependence of the propagation rate coefficient on the ionic strength for the propagation reaction between a charged monomer and a charged radical. With reference to the kinetic scheme in eq 6, with A for AAm and B
(20) F
DOI: 10.1021/acs.macromol.5b01148 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules for DMAEA-Q, the rate coefficient kp,BB only will exhibit the ionic strength dependence: therefore, the discussion hereinafter is focused on the homopropagation of DMAEA-Q. Let us consider the radical chain-end of a propagating chain, where the charged moiety of the terminal unit of DMAEA-Q is centered in the origin of the radial coordinate system shown in Figure 8.
Setting r ̅ = a (distance at which the reaction between the charged moieties of radical and monomer takes place), eq 25 gives ϕ 4πD
∫a
⎛ V (r ) ⎞ ⎛ V ⎞ 1 exp⎜ ⎟ dr = C∞ − Ca exp⎜ a ⎟ 2 r ⎝ kBT ⎠ ⎝ kBT ⎠
∞
(26)
where Ca is the monomer concentration at the reaction interface and Va the corresponding potential energy due to the electrostatic repulsive interaction. An analogue of eq 26 has been developed within the Derjaguin−Landau−Verwey−Overbeek (DLVO) theory to describe the steady-state flow of charged particles toward a reference particle in the context of reaction-limited aggregation of colloids. In that case, Ca = 0 (with a equal to the particle diameter if aggregation happens between particles of the same size) due to the particle “disappearance” after a successful aggregation event.38 On the contrary, here the concentration of species at the selected interface is not zero, and it can be evaluated by equating the net local flux to the propagation rate, which is in turn function of the intrinsic propagation rate coefficient kp,BB,i:
ϕ=
kp , BB , iCa NA
(27)
where NA is the Avogadro number. The monomer concentration at the interface is evaluated combining eqs 26 and 27: Figure 8. Graphical representation of the approach of a charged monomer molecule to the active site of the charged terminal unit of a radical chain. The qualitative profile of monomer concentration (C) as a function of the distance r between the charged groups ranging from the bulk (r → ∞) to the reaction interface (r = a) is shown.
exp
C(r ) dV (r ) kBT dr
dC(r ) dr
∫r ̅
∞
∞ 1 r2
exp
( ) dr V (r ) kBT
(28)
(29)
(30)
Accordingly, the observed propagation rate coefficient is expressed as a function of two contributions:
(22)
(23)
⎛ V ⎞ kp , BB ,0 = kp , BB , i exp⎜ − a ⎟ ⎝ kBT ⎠
(31)
⎡ kDLVO = 4πDNA ⎢ ⎢⎣
(32)
∫a
∞
−1 ⎛ V (r ) ⎞ ⎤ 1 ⎥ exp d r ⎜ ⎟ r2 ⎝ kBT ⎠ ⎥⎦
Equations 31 and 32 provide the reaction-controlled and diffusion-controlled propagation rate coefficients, respectively. A more convenient form to express the latter contribution comes from the DLVO theory and involves the so-called Fuchs stability ratio (W), which in the present case is defined as follows:
(24)
Equation 24 can be integrated using the boundary conditions V(r → ∞) = 0 and C(r → ∞) = C∞, where C∞ is the bulk monomer concentration: ϕ 4πD
∫a
−1 ⎛ 1 1 ⎞⎟ ⎜ kp , BB = ⎜ + kDLVO ⎟⎠ ⎝ kp , BB ,0
Combining eqs 21−23, the following final expression results: ⎛ C(r ) dV (r ) dC(r ) ⎞ ϕ = 4πr 2D⎜ + ⎟ dr ⎠ ⎝ kBT dr
4πDNA
which leads to the following key formula:
where C is the monomer concentration profile and D its molecular diffusivity. On the other hand, the diffusive flux can be expressed according to Fick’s first law: JD = −D
kp , BB , i
kp , BBC∞ = kp , BB , iCa
(21)
where JC and JD are the convective and diffusive fluxes per unit surface, respectively. The local convective flux associated with the electrostatic field and accounting for the friction forces due to the medium can be expressed as a function of the gradient of potential energy of the total electrostatic interaction (V): JC = −D
( )+ Va kBT
Finally, the observed propagation rate coefficient kp,BB, referred to the bulk monomer concentration, is expressed imposing flux continuity from the bulk to the reaction interface:
The total flux ϕ of monomer molecules approaching the radical trough a spherical surface of radius r is defined as ϕ = −4πr 2(JC + JD )
C∞
Ca =
W=a
⎛ V (r ) ⎞ ⎛ V(r ) ⎞ 1 ̅ ⎟ exp⎜ ⎟ dr = C∞ − C( r ̅ ) exp⎜ 2 r ⎝ kBT ⎠ ⎝ kBT ⎠
∫a
∞
⎛ V (r ) ⎞ k 1 exp⎜ ⎟ dr = DLCA ≥ 1 2 kDLVO r ⎝ kBT ⎠
(33) 38
where kDLCA is the fast, diffusion-limited aggregation rate. In comparison with colloidal particle aggregation, here the stability ratio represents the extent of the limitation to the monomer
(25) G
DOI: 10.1021/acs.macromol.5b01148 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
results in Figure 6 suggest that the dependence of the composition behavior upon the electrolyte concentration is relevant at all w0M values explored in the present study: therefore, a fully reaction-limited regime with kp,BB independent of Ce is never established in the specific system under examination. Reactivity Ratios. Equations 12−19 involve a large number of rate coefficients, which can be expressed through conveniently defined reactivity ratios. Specifically, each rate coefficient corresponding to a secondary reaction involving a radical of type i is divided by the corresponding homopropagation rate coefficient kp,ii, while the conventional propagation reactivity ratios are defined as in eqs 8 and 9 with kp,BB function of the electrolyte concentration. Note that when all the model equations are rewritten in terms of reactivity ratios, also the ratio between the two homopropagation rate coefficients (q) needs to be introduced. The complete list of reactivity ratios, including also those corresponding to secondary reactions, is provided in Table 2.
diffusion toward the radical as a function of the strength of the repulsive forces acting between the approaching species. According to eq 33, if the electrostatic repulsion is negligible (V → 0), the monomer diffusion contribution reduces to kDLCA = 4πaDNA and does not suffer any electrostatic limitation (it depends on monomer diffusivity only). The accurate evaluation of W requires the knowledge of the potential energy function, which is usually not available. Therefore, an empirical approach has been applied to evaluate the stability ratio as a function of the electrolyte concentration (Ce) through the formula W = k1(Ce)−α
(34)
where α and k1 are fitting parameters which account also for the type of electrolyte.39 Combining eqs 33 and 34, a convenient expression of the DLVO term is found: kDLVO =
kDLCA = kDLVO ,0(Ce)α W
(35)
Plugging this equation into eq 30, the final relationship for the propagation rate coefficient of DMAEA-Q as a function of the electrolyte concentration is obtained: ⎛ 1 ⎞−1 1 ⎜ ⎟ kp , BB = ⎜ + kDLVO ,0(Ce)α ⎟⎠ ⎝ kp , BB ,0
Table 2. Complete List of Reactivity Ratios Corresponding to the Reactions Introduced by the Composition Model with Secondary Reactions (cf. Kinetic Schemes in Eqs 6, 10, and 11)
(36)
Depending on the extent of the electrostatic screening of the repulsive forces between charged units, two limiting cases can be defined based on eq 36: (I) If the electrolyte concentration is large (i.e., high monomer or salt concentration), the diffusion limitations to the propagation rate become negligible and the propagation event is reaction-limited: accordingly, kp,BB reduces to kp,BB,0. With reference to eq 31, the intrinsic propagation kinetics is practically independent of the electrolyte concentration: owing to the strong electrostatic screening, the potential energy profile is flattened as well as its value at the interface, so that the exponential term in the formula approaches 1. (II) If the electrolyte concentration is small (e.g., at low monomer concentration and in the absence of salt addition), the diffusion limitation is increased and the process becomes diffusion-limited: kp,BB reduces to kDLVO,0(Ce)α and exhibits the electrolyte concentration dependence typical of the electrostatic-driven diffusion term. Under these conditions the intrinsic reactivity term is much less relevant, and its dependence on Va (generally a function of Ce) is not relevant as well. These two limiting cases lead to the definition of the propagation rate coefficient of DMAEA-Q as a function of three parameters (cf. eq 36): kp,BB,0, which reflects the intrinsic propagation kinetics; kDLVO,0 and α, which account for the electrostatic effect. With reference to eqs 33 and 35, the stability ratio is by definition equal to 1 when the electrolyte concentration is large enough to achieve the complete electrostatic screening of the repulsive forces; in this case, the rate of diffusion is the highest possible, and the electrolyte concentration corresponds to the so-called critical coagulation concentration (CCC) in colloidal science. Consequently, eq 36 and the corresponding parameters are meaningful as long as Ce ≤ CCC: when the electrolyte concentration is larger than the critical coagulation value, Ce in eq 36 is simply set constant and equal to the critical value. On the other hand, the experimental
Among the 11 reactivity ratios in Table 2, only those involving kp,BB are functions of the electrolyte concentration. Additionally, the rate coefficient of MCR propagation of DMAEA-Q, which involves as well the interaction between two charged species, exhibits the following dependence on the electrolyte concentration: kpT, BB H
⎛ ⎞−1 1 1 ⎜ ⎟ =⎜ T + kDLVO ,0(Ce)α ⎟⎠ ⎝ kp , BB ,0
(37)
DOI: 10.1021/acs.macromol.5b01148 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules This equation has been developed considering an intrinsic propagation coefficient specific of the reaction involving an MCR (kTp,BB,0), which is generally orders of magnitude smaller than kp,BB,0. On the other hand, the diffusive contribution due to the electrostatic repulsion has been defined in the same way for the two types of radicals: this is indeed a reasonable assumption, since the difference in electronic density and reactivity between chain-end and midchain radical is expected not to interfere significantly with the electrostatic interaction between the corresponding charged groups. Given such limitations and assumptions, the reactivity ratios defined previously can be expressed as functions of monomer and electrolyte concentrations, as detailed again in Table 2. There, the coefficients An denote the reactivity ratios or terms independent from the electrolyte concentration, while Bn are the coefficients of the electrostatic interaction terms (the subscript n refers to the numbering of the reactivity ratios as they are listed in the table). Eventually, tBB,i is the ratio between the intrinsic propagation rate coefficients of midchain and chain-end radicals of DMAEA-Q. These reactivity ratios involve 18 fitting parameters and can be introduced in the previous system of equations, thus obtaining the following final form of the model equations: −
RAfB
+
rA
RBfA
tBAQ BfA
− bAAFARA − bABFBRA + tAAQ AfA +
rBq
q
Bn = A n
RBfA rBq
+
RAfB rA
=0
bBAFARB − tAAQ AfA − tABQ AfB = 0 q
(40)
RA + RB + Q A + Q B = 1
(
fA RA +
FA =
(
fA RA +
RB rBq
+ tAAQ A +
(41) RB rBq
tBAQ B
+ tAAQ A +
)+f ( B
q
RB q
tBAQ B q
+
RA rA
) +
tBBQ B q
)
+ tABQ A
(42) df A dχ
=
×
fA fB χ−1 RA +
(
fA RA +
RB rBq RB rBq
+ tAAQ A + + tAAQ A +
tBAQ B q tBAQ B q
−
RB q
−
)+f ( B
RB q
RA rA
+
− RA rA
tBBQ B q
+
− tABQ A
tBBQ B q
(44)
RESULTS AND DISCUSSION As anticipated, the developed model has been validated by comparison with the experimental results of all experiments in Table 1. Since both DMAEA-Q and NaCl are 1:1 electrolytes, the initial value of the overall electrolyte concentration corresponds to the initial value of the ionic strength. Therefore, all functional dependences on Ce in the model equations will be directly expressed as dependences on ionic strength; accordingly, the electrostatic interaction parameters have been estimated hereinafter with Ce expressed in terms of molality (mol kg−1). Given the definition of ionic strength, such macroscale property can be used to quantify the screening of the electrostatic interactions by dissociated electrolytes. In the generic experiment, the polymerization reaction modifies the spatial distribution of ionic charges in the system and their degrees of freedom with respect to the initial conditions (i.e., position and mobility of the charged units incorporated into the polymer chains are different from that of the free monomer). Therefore, the impact of the ions on the reactivity is likely to change during the polymerization and the effective ionic strength should change accordingly. A detailed description of the electrostatic interactions involving ions in a polymer system at the molecular level (e.g., charge interactions in the neighborhood of radical chain-end and approaching monomer) and, more importantly, of their correlation to macroscale parameters such as monomer conversion and ionic strength is not easy and certainly beyond the scope of the present work. Therefore, three simplified limiting cases have been considered to determine an effective value of Ce. (I) The effective concentration of free ions, those which contribute to the electrostatic screening of the charges during the propagation step, is evaluated accounting for the total ions coming from the added salt (equal to C0S), the total counterions from DMAEA-Q, and only the DMAEA-Q cations belonging to unconverted monomer:
(39)
bAAFARA +
B2 A2
■
tBBQ BfB bBBFBRB b FR − BA A B + + tABQ AfB = 0 q q q
−
kp , BB ,0
= An
which holds for n = 3, 6, 7, 10, and 11 (where A10 = 1). This way, the total number of parameters to be evaluated by direct fitting is reduced to 11. Such evaluation has been performed by numerical optimization (minimization of the discrepancies between model predictions and experiments in terms of monomer composition as a function of conversion for all experiments in Figures 5−7).
(38) −
kDLVO ,0
)
+ tABQ A
(43)
Note that in these equations the radical concentrations are expressed as mole fractions. Equations 38−43 are a set of mixed algebraic-differential equations whose numerical solution is performed as a function of conversion given the initial conditions (w0M or M0, f0A). As usual, the real issue of this type of modeling is the meaningful evaluation of the many involved parameters. The values of the reactivity ratios corresponding to AAm homopolymerization have been estimated from unpublished data of the individual rate coefficients of kp,AA,40 kbb,AA, and kTp,AA.41 Accordingly, tAA = 0.299 × 10−3 (parameter A8) and bAAM = 0.356 × 10−3 (parameter A4) at 50 °C. Moreover, focusing on the final expressions of the reactivity ratios in Table 2, a correlation between each pair of parameters An and Bn applies. Specifically
Ce = CS0 +
1 0 1 0 CB + CB(1 − χB ) 2 2
(45)
(II) If counterion condensation is considered, under the tightest conditions of complete counterion condensation on all the charged monomer units in the polymer chains, only the contribution of free DMAEA-Q charged units and of the corresponding counterions is effective: Ce = CS0 + CB0(1 − χB )
(46)
(III) Assuming that the local effect of the charge distribution is function of the total charges only, the ionic strength can be approximated to its initial value: Ce = Ce0 = CS0 + CB0 I
(47) DOI: 10.1021/acs.macromol.5b01148 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules In the equations above, χB is the molar conversion of monomer B. All the previous expressions of the electrolyte concentration can be actually represented by the following general equation: Ce = CS0 + CB0[1 − χB (1 − η)]
(48)
which involves the novel fitting parameter η. Therefore, eq 48 has been used in order to maintain some degree of freedom in the evaluation of the electrolyte concentration, even though at the cost of an additional fitting parameter. As anticipated, despite the several underlying assumptions, a large number of parameters need to be estimated: therefore a sequential fitting strategy has been implemented. All optimizations have been carried out through a genetic algorithm (GA), in particular using the “ga” function in Matlab. In the first optimization step, the secondary reactions are neglected and the electrostatic interaction parameters are evaluated. The model equations reduce to the single eq 7, with rA and rB defined as in Table 2 and Ce as in eq 48. The resulting parameter values are reported in Table 3, while the corresponding model predictions are compared with the experimental data in Figure 9.
Figure 9. Comparison between experimental data (symbols) and model simulation results (lines) of residual monomer mixture composition as a function of conversion for the copolymerization reactions of AAm with DMAEA-Q at 50 °C. Top left: w0M = 10% (runs 1−6 in Table 1); top right: w0M = 20% (runs 7−12); bottom left: low monomer concentrations with w0M as in Figure 6 (runs 13−15, 4, and 10); bottom right: reactions with addition of NaCl with w0M as in Figure 7 (runs 16−19). Simulation results neglecting secondary reactions and with parameter values as in Table 3. The error ε between simulated and experimental data corresponding to each set of results is indicated (overall error ε = 0.026%).
Table 3. Results of the First Optimization Step (Model without Secondary Reactions) parameter
optimized value
optimization range
A1 A2 B2 α η
0.51 1.28 1.19 0.85 0.98
0.1−2.0 0.1−5.0 0.1−5.0 0.1−2.0 0−1
ri =
The simulation results show that the model is reproducing nicely the experimental results in a wide range of values of initial monomer concentration and initial ionic strength. As expected, it is impossible to fit properly the behavior of the experimental curves in the cases of salt addition without accounting for the secondary reactions. Nevertheless, the contribution of the electrostatic effect, which proves to be properly developed in the model, appears to be the most relevant mechanism underlying the unconventional composition behavior of the system. About the functional dependence of the ionic strength on conversion, the optimal value of the parameter η is very close to unity. This result suggests that an effective electrolyte concentration, which does not depend on monomer conversion but remains constant and equal to the initial value, is a reasonable approximation. Therefore, eq 47 is used to evaluate Ce in all the model simulations reported in the following, and the calculated values of Ce are reported in Table 1. In the second optimization step, the reactivity ratios rA and rB are kept constant and equal to the values in Table 3; on the other hand, all the remaining parameter values are estimated using the same optimization algorithm mentioned above. Since the secondary reactions are included, eqs 38−43 with the reactivity ratios as in Table 2 are used in the model. In order to further reduce the number of parameters to be estimated, an additional assumption has been introduced: the same value of the propagation reactivity ratio ri applies to chain-end as well as midchain radicals, that is
kp , ii kp , ij
≅
kpT, ii kpT, ij
(49)
Accordingly, the reactivity ratios tAB and tBA can be evaluated as follows:
tAB =
tAA rA
(50)
tBA =
tBB rB
(51)
This way, the parameters to be determined reduce to those in Table 4, where the estimated values resulting from the second optimization step are reported, while the corresponding model simulations are shown in Figure 10. The calculated curves fit appreciably well the experimental data through all the range of compositions and initial monomer concentrations. Moreover, the effect of secondary reactions on the composition behavior of the curves at constant ionic Table 4. Results of the Second Optimization Step (Model with Secondary Reactions) parameter A3 A5 A6 A7 tBB,i J
optimized value 0.27 2.37 5.08 2.16 2.97
× × × ×
10−2 103 102 10−2
optimization range 0.1−10 10−4−10−1 10−104 102−104 10−4−10−1 DOI: 10.1021/acs.macromol.5b01148 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
copolymer composition as a function of conversion. In addition, secondary reactions of backbiting and MCR propagation have been included due to the acrylic nature of the two monomers. The dependence of the reactivity ratios on the ionic strength has been introduced applying the DLVO theory to the propagation of DMAEA-Q: accordingly, an effective rate coefficient reproducing the reaction-limited as well as the diffusion-limited propagation regimes has been proposed. The developed rate law is combined with the definition of reactivity ratios of propagation and backbiting reactions to define a kinetic model capable of predicting the composition behavior of the copolymer system as a function of monomer and electrolyte concentration. The many model parameters have been evaluated by fitting the model predictions to all the available experimental data. The developed model together with the estimated parameters is capable of nicely reproducing the experimental results and exhibits the correct functionality on the initial ionic strength. In addition, the model simulations revealed that the effect of secondary reactions on the composition behavior of the investigated system is negligible, while the composition drift is controlled by the electrostatic effect. The proposed approach to characterize and simulate the composition behavior of a polyelectrolyte system is presumed to be general enough to be applied to other copolymers of interest where one or more ionic monomers are involved.
Figure 10. Comparison between experimental data (symbols) and model simulation results (lines) of residual monomer mixture composition as a function of conversion for the copolymerization reactions of AAm with DMAEA-Q at 50 °C. Top left: w0M = 10% (runs 1−6 in Table 1); top right: w0M = 20% (runs 7−12); bottom left: low monomer concentrations with w0M as in Figure 6 (runs 13−15, 4, and 10); bottom right: reactions with addition of NaCl with w0M as in Figure 7 (runs 16−19). Simulation results including secondary reactions and with parameter values as in Tables 3 and 4. The error ε between simulated and experimental data corresponding to each set of results is indicated (overall error ε = 0.023%).
■
AUTHOR INFORMATION
Corresponding Author
*E-mail
[email protected]; Tel +41 44 632 66 60 (G.S.). Notes
The authors declare no competing financial interest.
■
strength is nicely captured by the model. However, the overall performances of the model in reproducing the experimental data are not significantly improved by the introduction of secondary reactions. Therefore, it can be concluded that secondary reactions do not play a major role in determining the composition behavior of a copolymer system as long as realistic values of rate coefficients are considered for such reactions, as it is the case for the investigated system.
ACKNOWLEDGMENTS The authors thank BASF for the financial support in the framework of the General Research Agreement between ETH Zürich and BASF as well as the project partners for the technical discussions. Moreover, the authors thank Dr. R. Verel and D. Sutter at D-MATL, ETH Zürich, for their support with the NMR facility.
■
■
CONCLUSIONS The copolymerization of acrylamide with the cationic monomer DMAEA-Q has been investigated by in situ 1H NMRa characterization technique providing very accurate data of residual monomer mixture composition as a function of conversion for a wide range of reaction conditions. Interestingly, the results showed that the composition behavior of the system exhibits a strong dependence upon the initial monomer mixture concentration, which results in a composition dependence of the reactivity ratios. Further experiments with salt addition (NaCl) revealed that the observed monomer concentration dependence can be largely explained in terms of a dependence on the ionic strength. This behavior is consistent with the proposed mechanism of an electrostatic effect on reaction kinetics: the repulsion forces between the charged species of DMAEA-Q reduce the effective propagation rate; at the same time the repulsion forces between the charges are screened by the addition of electrolytes to the aqueous solution. This electrostatic effect has been considered in the development of a model simulating the evolution of the
REFERENCES
(1) Tripathy, S. K.; Kumar, J.; Nalwa, H. S. Handbook of Polyelectrolytes and Their Applications; ASP: Stevenson Ranch, CA, 2002. (2) Goin, J. Water Soluble Polymers; CEH Marketing Research Report 582.0000 D-E, SRI International, 1991. (3) Manning, G. S. Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties. J. Chem. Phys. 1969, 51, 924−933. (4) Oosawa, F. Polyelectrolytes; Marcel Dekker: New York, 1971. (5) Dragan, S.; Ghimici, L.; Wandrey, C. Charge Density, Solvent Polarity and Counterion Nature Effects on the Solution Properties of Some Polycations. Macromol. Symp. 2004, 211, 107−119. (6) Gonzalez Garcia, G.; Kreft, T.; Alb, A. M.; de la Cal, J. C.; Asua, J. M.; Reed, W. F. Monitoring the Synthesis and Properties of Copolymeric Polycations. J. Phys. Chem. B 2008, 112, 14597−14608. (7) Ishikawa, T.; Kikuchi, M.; Kobayashi, M.; Ohta, N.; Takahara, A. Chain Conformation of Poly[2-(methacryloyloxy)ethyltrimethylammonium chloride] in Aqueous Sodium Chloride Solutions. Macromolecules 2013, 46, 4081−4088. (8) Mabire, F.; Audebert, R.; Quivoron, C. Synthesis and Solution Properties of Water Soluble Copolymers Based on Acrylamide and
K
DOI: 10.1021/acs.macromol.5b01148 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules Quaternary Ammonium Acrylic Comonomer. Polymer 1984, 25, 1317−1322. (9) Nicke, R. Flocculating Agents Help to Increase the Production. Zellst. Papier 1982, 31, 19−23. (10) Zhao, Y.; Lord, M. S.; Stenzel, M. H. A Polyion Complex Micelle with Heparin for Growth Factor Delivery and Uptake into Cells. J. Mater. Chem. B 2013, 1, 1635−1643. (11) Wagner, E. Polymers for siRNA Delivery: Inspired by Viruses to be Targeted, Dynamic, and Precise. Acc. Chem. Res. 2012, 45, 1005− 1013. (12) Baade, W.; Hunkeler, D.; Hamielec, A. E. Copolymerization of Acrylamide with Cationic Monomers in Solution and InverseMicrosuspension. J. Appl. Polym. Sci. 1989, 38, 185−201. (13) Losada, R.; Wandrey, C. Copolymerization of a Cationic Double-Charged Monomer and Electrochemical Properties of the Copolymers. Macromolecules 2009, 42, 3285−3293. (14) Tanaka, H. Copolymerization of Cationic Monomers with Acrylamide in an Aqueous Solution. J. Polym. Sci., Part A: Polym. Chem. 1986, 24, 29−36. (15) Rabinowitz, R.; Marcus, R.; Pellon, J. Free Radical Homopolymerization and Copolymerization of Vinyl Phosphines, Oxides, and Sulfides. J. Polym. Sci., Part A: Gen. Pap. 1964, 2, 1233− 1240. (16) Vasilev, K.; Cook, J.; Griesser, H. J. Antibacterial Surfaces for Biomedical Devices. Expert Rev. Med. Devices 2009, 6, 553−567. (17) Hunkeler, D.; Hamielec, A. E.; Baade, W. The Polymerization of Quaternary Ammonium Cationic Monomers with Acrylamide. Adv. Chem. Ser. 1989, 175−192. (18) Losada, R.; Wandrey, C. Non-Ideal Polymerization Kinetics of a Cationic Double Charged Acryl Monomer and Solution Behavior of the Resulting Polyelectrolytes. Macromol. Rapid Commun. 2008, 29, 252−257. (19) Hernandez-Barajas, J.; Hunkeler, D. Copolymers of Acrylamide and Quaternary Ammonium Cationic Monomers: Characterization by HPLC and Copolymer Composition Control. Ber. Bunsen Ges. Phys. Chem. 1996, 100, 723−729. (20) Gonzalez, G.; de la Cal, J. C.; Asua, J. M. Synthesis of Cationic Flocculants in Continuous Reactors. Chem. Eng. J. 2010, 162, 753− 759. (21) Ni, H. F.; Hunkeler, D. Prediction of Copolymer Composition Drift Using Artificial Neural Networks: Copolymerization of Acrylamide with Quaternary Ammonium Cationic Monomers. Polymer 1997, 38, 667−675. (22) Hernandez-Barajas, J.; Hunkeler, D. Inverse-Emulsion Copolymerization of Acrylamide and Quaternary Ammonium Cationic Monomers with Block Copolymeric Surfactants: Copolymer Composition Control Using Batch and Semi-Batch Techniques. Polymer 1997, 38, 449−458. (23) Riahinezhad, M.; Kazemi, N.; McManus, N.; Penlidis, A. Effect of Ionic Strength on the Reactivity Ratios of Acrylamide/Acrylic Acid (sodium acrylate) Copolymerization. J. Appl. Polym. Sci. 2014, 131, 40949. (24) McCormick, C. L.; Salazar, L. C. Water-Soluble Copolymers. 41. Copolymers of Acrylamide and Sodium 3-Acrylamido-3-methylbutanoate. J. Macromol. Sci., Part A: Pure Appl.Chem. 1992, 29, 193−205. (25) Lacik, I.; Ucnova, L.; Kukuckova, S.; Buback, M.; Hesse, P.; Beuermann, S. Propagation Rate Coefficient of Free-Radical Polymerization of Partially and Fully Ionized Methacrylic Acid in Aqueous Solution. Macromolecules 2009, 42, 7753−7761. (26) Drawe, P.; Buback, M.; Lacik, I. Radical Polymerization of Alkali Acrylates in Aqueous Solution. Macromol. Chem. Phys. 2015, 216, 1333−1340. (27) Kurenkov, V. F.; Nadezhdin, I. N.; Antonovich, O. A.; Lobanov, F. I. Phase Separation in Aqueous Solutions of Binary Copolymers of Acrylamide with Sodium 2-Acrylamido-2-Methylpropanesulfonate and Sodium Acrylate. Russ. J. Appl. Chem. 2004, 77, 804−808. (28) Preusser, C.; Hutchinson, R. A. An In-Situ NMR Study of Radical Copolymerization Kinetics of Acrylamide and Non-Ionized
Acrylic Acid in Aqueous Solution. Macromol. Symp. 2013, 333, 122− 137. (29) Junkers, T.; Barner-Kowollik, C. The Role of Mid-Chain Radicals in Acrylate Free Radical Polymerization: Branching and Scission. J. Polym. Sci., Part A: Polym. Chem. 2008, 46, 7585−7605. (30) Plessis, C.; Arzamendi, G.; Alberdi, J. M.; Van Herk, A. M.; Leiza, J. R.; Asua, J. M. Evidence of Branching in Poly(butyl acrylate) Produced in Pulsed-Laser Polymerization Experiments. Macromol. Rapid Commun. 2003, 24, 173−177. (31) Nikitin, A.; Hutchinson, R. A.; Buback, M.; Hesse, P. Determination of Intramolecular Chain Transfer and Midchain Radical Propagation Rate Coefficients for Butyl Acrylate by Pulsed Laser Polymerization. Macromolecules 2007, 40, 8631−8641. (32) Tanaka, K.; Yamada, B.; Fellows, C. M.; Gilbert, R. G.; Davis, T. P.; Yee, L. H.; Smith, G. B.; Rees, M. T. L.; Russell, G. T. Pulsed-laser Polymerization-Gel Permeation Chromatographic Determination of the Propagation-Rate Coefficient for the Methyl Acrylate Dimer: a Sterically Hindered Monomer. J. Polym. Sci., Part A: Polym. Chem. 2001, 39, 3902−3915. (33) Barth, J.; Buback, M.; Hesse, P.; Sergeeva, T. Termination and Transfer Kinetics of Butyl Acrylate Radical Polymerization Studied via SP-PLP-EPR. Macromolecules 2010, 43, 4023−4031. (34) Barner-Kowollik, C.; Günzler, F.; Junkers, T. Pushing the Limit: Pulsed Laser Polymerization of n-Butyl Acrylate at 500 Hz. Macromolecules 2008, 41, 8971−8973. (35) Cuccato, D.; Dossi, M.; Moscatelli, D.; Storti, G. Quantum Chemical Investigation of Secondary Reactions in Poly(vinyl chloride) Free-Radical Polymerization. Macromol. React. Eng. 2012, 6, 330−345. (36) Mayo, F. R.; Lewis, F. M. Copolymerization. I. A Basis for Comparing the Behavior of Monomers in Copolymerization; The Copolymerization of Styrene and Methyl Methacrylate. J. Am. Chem. Soc. 1944, 66, 1594−1601. (37) Skeist, I. Copolymerization: the Composition Distribution Curve. J. Am. Chem. Soc. 1946, 68, 1781−1784. (38) Berg, J. C. An Introduction to Interfaces & Colloids: The Bridge to Nanoscience; World Scientific Publishing Co. Pte. Ltd.: Singapore, 2010. (39) Reerink, H.; Overbeek, J. T. G. The Rate of Coagulation as a Measure of the Stability of Silver Iodide Sols. Discuss. Faraday Soc. 1954, 18, 74−84. (40) Chovancova, A.; Lacik, I. Confidential data. (41) Kattner, H.; Buback, M. Confidential data.
L
DOI: 10.1021/acs.macromol.5b01148 Macromolecules XXXX, XXX, XXX−XXX
