Kinetic Model and Synthesis of Hyperbranched Polyurethane

Jun 7, 2019 - The hyperbranched polyurethane acrylates (HBPUAs) contain a large ... lower than that of linear oligomers with the same molecular weight...
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Article Cite This: Ind. Eng. Chem. Res. 2019, 58, 11763−11769

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Kinetic Model and Synthesis of Hyperbranched Polyurethane Acrylates from Monomers A2 and B3 with End-Capping Molecules BR Kuo-Chung Cheng,* Wei-Chih Chen, and Pei-Shan Cheng Department of Chemical Engineering and Biotechnology, National Taipei University of Technology, Taipei 106, Taiwan

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S Supporting Information *

ABSTRACT: The preparation of hyperbranched polymers by the polymerization of monomers A2 and B3 with monofunctional monomers BR was investigated by recursive and kinetic models. A diagram of the gel and sol regions corresponding to the composition of the monomers was proposed. According to the kinetic model, the average degree of polymerization and the degree of branching (DB) that are dependent on the conversion and initial compositions of the reactants were calculated by a generating function method. If the molar ratio of B3/A2/BR was 1:3:3, then polymers with a weight-average degree of polymerization of 171 and a DB of 0.97 could be obtained at a conversion of 0.99. Polyurethane acrylates were further prepared from various mixtures of trimethylolpropane ethoxylate (B3), hexamethylene diisocyanate (A2), and hydroxyethyl acrylate (BR). The molecular weights of the polymers predicted by the model were in good agreement with those determined by gel permeation chromatography.

■

simulations.16 However, the calculation results were also dependent on the MC simulation size, which had a limited number of the reactants during polymerization. In our previous work, the plot of gel and sol regions at a high conversion shows that the dependence on the initial composition of the monomers was proposed based on the recursive and kinetic models. The molecular weight and degree of branching (DB) of HBPs prepared via polymerization of monomers A2 and Bg (g > 2) could be manipulated by choosing different monomer compositions and feeding rate of the end-capping molecule (AR).17,18 HBPs without a gel fraction at a high conversion can be prepared via the polymerization of monomers A2 and Bg by adding AR into the reactor. An HBP containing polyethylene glycol (PEG) and aliphatic chains was synthesized by bulk polymerization of a diepoxide with a primary amine in the presence of a monoepoxide. The flexibility and impact strength of the polylactide (PLA) composite can be improved by adding the HBP. The hyperbranched polyester polymer was prepared from a mixture of trimethylopropane triglycidyl ether, adipic acid, and heptanoic acid, which could increase the viscoelastic stability of the tissue conditioner used to treat lesions caused by ill-fitting dentures.19,20 Polyurethane acrylates (PUAs) have outstanding chemical resistance and mechanical properties and have been widely used as UV-curable coatings. The hyperbranched polyurethane

INTRODUCTION Because dendrimers and hyperbranched polymers (HBPs) have highly branched structures and a large amount of peripheral, pending, or side functional groups, they possess very unique properties that are different from those of linear polymers, such as high solubility, relatively low entanglement, and low viscosity.1−4 Although the hyperbranched polymers have a less regular structure than that of dendrimers with a well-defined shape and a perfectly regular structure, the HBPs can be synthesized by other facile methods rather than the complicated multiple-step reactions used for dendrimer preparation.5,6 HBPs can be generally produced by a singlemonomer methodology (SMM), such as stepwise polymerization of ABg-type monomers with g > 2, self-condensing vinyl polymerization (SCVP), and proton-transfer polymerization (PTP).7−10 The available commercial monomers are very limited, whereas multifunctional monomers or resins, such as A2 and Bg (g > 2), containing versatile groups are more readily accessible. Therefore, to overcome the disadvantage of the SMM, HBPs can be prepared via the stepwise polymerization of two types of monomers, A2 and Bg. However, it is necessary to choose an appropriate initial composition of monomers or stop the reaction at a low conversion to avoid forming a gel during polymerization.11−15 The branched poly(ether ester)s prepared by the condensation of the monomers A2 and B3 were investigated by using the experiments and Monte Carlo (MC) simulations. The effects of cyclization, unequal reactivity ratios of the groups, and the end-capping agents that reacted with group B from the core monomer B 3 were discussed by MC © 2019 American Chemical Society

Received: Revised: Accepted: Published: 11763

January 21, 2019 May 9, 2019 June 7, 2019 June 7, 2019 DOI: 10.1021/acs.iecr.9b00351 Ind. Eng. Chem. Res. 2019, 58, 11763−11769

Article

Industrial & Engineering Chemistry Research

completely, the polymerization stops and gelation does not occur. Therefore, branched polymers without a gel can be prepared in the range “I” shown in Figure 1. If r < 1, the initial

acrylates (HBPUAs) contain a large number of acrylic groups and have a viscosity lower than that of linear oligomers with the same molecular weight. HBPUAs can form networks with a higher cross-linking density than that of the traditional bifunctional cross-linking reagent.21−24 A coating or film with superior mechanical properties and chemical resistance can be obtained by the addition of HBPUAs. It is possible to produce HBPUAs via a stepwise polymerization of the mixture of monomers A2 and Bg (g > 2) with end-capping molecules. In this study, we planned to choose a more readily commercialized combination of monomers: diisocyanate (A2) and triol monomer (B3) with addition of the end-capping molecule containing acrylate to synthesize the HBPUAs. Because the economic compound containing isocyanate and acrylate, AR, was lacking, another compound, 2-hydroxyethyl acrylate (HEA), was chosen as the alternating end-capping molecule. Note that the HEA, coded as BR, contains a hydroxyl group, B, which only can react with the isocyanate from the bifunctional monomer A2. Therefore, it is worth proposing a kinetic model to evaluate the synthesis of hyperbranched polymers from monomers A2 and B3 with end-capping molecules BR. First, the critical conversion that is dependent on the initial molar ratios of A2 and BR to B3 was derived from the recursive model. The changes in the degree of polymerization (DP) and the DB of the HBPs with the conversion under various compositions were calculated by the generating function method based on the kinetic model. Finally, the molecular weights of the synthesized polymers measured by gel permeation chromatography (GPC) were compared with those calculated by the theoretical model. Recursive Model. A stepwise polymerization system is considered with g (g > 2) functional B-type monomers, Bg, bifunctional A-type monomers, A2, and monofunctional B-type monomers, BR. The A groups can react with B, but A and B cannot react with themselves; thus, the two molecules can combine to form a large molecule. The initial mole ratios of the monomers A2 and BR to the monomer Bg are

Figure 1. Diagram of gel and 100% sol fraction regions dependent on the initial compositions of the reactants.

concentration of group A is less than that of B, pA > pB. In the region “IV”, that is, g + β1 > 2λ 2g (g − 1) , (pA)gel > 1. Even though the A groups reacted entirely, gelation could be avoided. Kinetic Model. We selected diisocyanate (A2) and triol monomer (B3) with 2-hydroxyethyl acrylate as the end-capping molecule (BR) to prepare the HBPUAs, in which the triol monomers are the core unit and g = 3. There are nine structural units, G(i), involved in this polymerization: G(1): B3 G(2): B2b∼ G(3): bBb∼ or Bb2∼ b G(4): ∼ ∼b > −b∼ or b3 G(5): A2 G(6): Aa∼ G(7): ∼aa∼ or a2 G(8): BR G(9): ∼bR G(10): Aa-bR G(11): Rb-a2-bR G(12): ∼a2-bR The reactions among the different units are

( )0

β1 = (BR)0 / Bg

( )0

λ 2 = (A 2)0 / Bg

(1)

where (A2)0, (Bg)0, and (BR)0 are the initial moles of the monomers A2, Bg, and BR, respectively. In this study, we focused on the work to propose ready models to evaluate the strategy of preparation of the hyperbranched polyurethane acrylate, and the effects of the configuration and conformation as well as intramolecular reactions are not considered in the calculation.25−27 Critical conversion of groups A and B, represented by pA and pB, can be calculated by the following equation based on the recursive model.28 r(pA2 )gel =

(pB2 )gel r

=

A 2 + B3 → Aa + B2b

A 2 + B2b → Aa + Bb2

g + β1 g (g − 1)

(2)

where r=

(3)

If the initial concentration of group A is greater than that of B, then r > 1, and pB > pA. As indicated in eq 2, when λ2 > 0.5g(g − 1), the (pB)gel > 1. When the B groups are consumed 11764

4kAB

G(5) + G(2) ⎯⎯⎯→ G(6) + G(3) 2kAB

A 2 + Bb2 → Aa + b3

G(5) + G(3) ⎯⎯⎯→ G(6) + G(4)

Aa + B3 → a 2 + B2b

G(6) + G(1) ⎯⎯⎯→ G(7) + G(2)

Aa + B2b → a 2 + Bb2

2(A 2)0 2λ 2 = (BR)0 + g (Bg )0 β1 + g

6kAB

G(5) + G(1) ⎯⎯⎯→ G(6) + G(2)

3kAB

2kAB

G(6) + G(2) ⎯⎯⎯→ G(7) + G(3) kAB

Aa + Bb2 → a 2 + b3

G(6) + G(3) ⎯→ ⎯ G(7) + G(4)

BR + A 2 → Aa − bR

G(8) + G(5) ⎯⎯⎯→ G(10)

BR + Aa → bR + a 2

G(8) + G(6) ⎯→ ⎯ G(9) + G(7)

2kAB

kAB

DOI: 10.1021/acs.iecr.9b00351 Ind. Eng. Chem. Res. 2019, 58, 11763−11769

Article

Industrial & Engineering Chemistry Research Table 1. Parameters of bij and ki b11 b21 b31 b41 b51 b61 b71 b81 b91 b10 1 b11 1 b12 1

b12 b22 b32 b42 b52 b62 b72 b82 b92 b10 2 b11 2 b12 2

b13 b23 b33 b43 b53 b63 b73 b83 b93 b10 3 b11 3 b12 3

BR + Aa − bR → Rb − a 2 − bR B3 + Aa − bR → B2b + a 2 − bR B2b + Aa − bR → Bb2 + a 2 − bR

Bb2 + Aa − bR → b3 + a 2 − bR

k1 k2 k3 k4 k5 k6 k7 k8 k9 k10 k11 k12

b14 b24 b34 b44 b54 b64 b74 b84 b94 b10 4 b11 4 b12 4

=

kAB

3kAB

G(1) + G(10) ⎯⎯⎯⎯→ G(2) + G(12) 2kAB

G(2) + G(10) ⎯⎯⎯⎯→ G(3) + G(12) kAB

G(3) + G(10) ⎯→ ⎯ G(4) + G(12)

or ki

(4)

The corresponding parameters, bij and ki, are shown in Table 1. A vector E is defined to characterize the molecule ⟨E⟩: E = (e1, e2 , e3, e4 , e5, e6 , e7 , e8, e9 , e7 , e8, e9 , e10 , e11, e12 , ew)

7 12 12 12

6kAB 4kAB 2kAB 3kAB 2kAB kAB 2kAB kAB kAB 3kAB 2kAB kAB

[E] = N (E)/N0

(8)

ki* = (ki /k 0)(V0/V )

(9)

d [E ] = dτ

(6)

where ⟨E′ + E″ + Li⟩ is the molecule formed by combining ⟨E′⟩ with ⟨E″⟩ in the ith reaction and

(10)

l o o

∑ ki*omoo 12

∑ ([E′][E″]p′i1p″i2 ) o E ′+ E ″+ Li = E n − [E]pi1 ∑ [E‴]p‴i2 −[E]pi2 ∑ [E‴]p‴i1 } i=1

all E‴

all E‴

(11)

Li = (l1 , l 2 , ..., l12 , 0)

where ∑all E denotes the sum over all possible values of vector E, and pij = eJ for bij = J. The one positive and two negative terms on the right side of eq 11 denote the total rates of appearance and disappearance of the isomer ⟨E⟩, respectively. This equation can be transformed into finite ordinary differential equations using a generating function.29 The profiles of the average DP of polymers and the fractions of the G(I) can be calculated as described in the Supporting Information. A modified DB based on the actual number over the maximum possible number of dendritic units is30

lJ = −δ(bi1 , J ) − δ(bi2 , J ) + δ(bi3 , J ) + δ(bi 4 , J ) J = l , 2, ..., 12

2 3 4 2 3 4

where N(E) is the number of isomers ⟨E⟩; V is the volume of the reaction system; N0, k0, and V0 are arbitrary reference numbers, the rate constant, and volume, respectively, and t is the reaction time. If the change in the volume of the reaction system is negligible, then according to eq 6, the rate equation of the isomers is

where eJ represents the number of structural units G(J), and ew, equaling e13, is the molecular weight of ⟨E⟩. For example, E = (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, W(B3)) denotes monomer B3, and W(B3) is the molecular weight; E = (0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, W(A2)) is A2, and W(A2) is the molecular weight of A2; and E = (0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, W(B3) + W(A2)) is the molecule Aa-bB2 formed by combining monomers A2 and B3. The reactions among molecules are ⟨E′⟩+⟨E″⟩ → ⟨E′ + E″ + Li⟩, i = 1, 2, ..., 12

6 6 6 7 7 7 10 9 11 2 3 4

τ = tk 0(N0/V0)

(5)

ki

1 2 3 1 2 3 5 6 10 10 10 10

E′ = (0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, W(A2)) E″ = (0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, W(B3) + W(A2)) L3 = (0, −1, +1, 0, −1, +1, 0, 0, 0, 0, 0, 0, 0) E′ + E′ + L3 = (0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2W(A2) + W(B3), and k2 = 4kAB Furthermore, a dimensionless number fraction, [E], the ratio of the reaction rate constant, ki*, and a scaled time, τ, are defined:

G(8) + G(10) ⎯→ ⎯ G(11)

G(bi1) + G(bi2) → G(bi3) + G(bi 4), i = 1, 2, ..., 12

5 5 5 6 6 6 8 8 8 1 2 3

(7)

in which δ(bij,J) is Kronecker delta: δ(bij , J ) = 1, for bij = J , and δ(bij , J ) = 0, for bij ≠ J

For instance, monomer A2 reacts with molecule Aa-bB2 by the following reaction:

DB =

A 2 + Aa‐b B2 → Aa‐b Bb − a A

in which ⟨E′⟩ = A2 ⟨E″⟩ = Aa-bB2 ⟨E′ + E″ + Li⟩ = Aa-bBb-aA

ND ND + 0.5NL

(12)

where ND and NL are the number of dendritic and linear units, respectively. In this study, three reacted B functionalities, b3, denote the dendritic units, and two reacted B functionalities, Bb2, represent the linear units. The numbers of dendritic 11765

DOI: 10.1021/acs.iecr.9b00351 Ind. Eng. Chem. Res. 2019, 58, 11763−11769

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Industrial & Engineering Chemistry Research

calculated by the kinetic model. The DPw of the system with the lower ratio of BR was found to increase more quickly than that with the higher one. Along the line “vz” in Figure 2, β1 was less than or equal to 3, and the critical conversion of group B was 100%, at which the DPw became infinite. For example, without the addition of BR, that is, β1 = 0, the critical conversions of A and B were 0.5, and 1, respectively, as shown in Figure 3b. The residue fraction of A2, [A2], was 0.1875. At β1 = 3, the critical conversion of A became 1, and all the monomers and BR reacted to form a gel. At a higher content of BR, such as β1 = 3.2 in the region IV, as shown in Figure 1, the critical conversion of A was greater than 1 according to eq 2. This result implied that the reaction had to stop at pA= 1 and that gelation could not occur during polymerization. Therefore, the DPw of the polymers was approximately 53 at pA= 1 and pB = 0.968. There were only a few unreacted BR units after polymerization, and [BR] = 0.0143. It is not easy to reach the full conversion for the practical preparation of polymers via stepwise polymerization. The DP of HBPs is dependent on the addition of various ratios of endcapping molecules BR near the full conversion of group A or B (e.g., 0.9, 0.95, and 0.99 at λ2 = 3), as shown in Figure 4. When

and linear units are changed with time and conversion, as calculated by the kinetic model. Another branched structural feature was proposed as the fraction of branch points, FB [10]: FB =

■

ND (total number of units) − (number of monomers) (13)

RESULTS AND DISCUSSION The gelation curves of the critical conversions of 0.9, 0.95, and 1 of the polymerization of monomers B3, A2, and BR are plotted in Figure 2. At r > 1, when λ2 > 3, on the right side of

Figure 2. Diagram of the gelation curves of critical conversion of 0.9, 0.95, and 1 dependent on the ratios of A2 and BR.

line vz, the branched polymers without gel can be obtained at pB = 1, where the polymerization stops automatically owing to the complete consumption of the B groups. If λ2 < 3, then gelation occurred before the B groups entirely reacted. For example, if λ2 = 2.43, then the gel formed at pB = 0.9. At r < 1, and β1 > (2 3λ 2 − 3), that is, on the left side of the curve vx, the branched polymers of 100% sol fraction can be prepared at pA = 1. The degree of polymerization that is dependent on the conversion was calculated by the kinetic model. Figure 3a shows the profiles of the weight-average degree of polymerization, DPw, dependent on reaction time at λ2 = 3, which was

Figure 4. Degree of polymerization changed with β1 and conversions of A or B at λ2 = 3.

r > 1, the DPn increased with increasing BR, but there were no apparent variances among the values of DPw at different

Figure 3. Profiles of degree of polymerization dependent on (a) time and (b) conversion at different ratios of BR at λ2 = 3. 11766

DOI: 10.1021/acs.iecr.9b00351 Ind. Eng. Chem. Res. 2019, 58, 11763−11769

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Industrial & Engineering Chemistry Research contents of BR. The end-capping molecule, BR, could react with the growing polymers containing groups A, resulting in the formation of dangling chains ∼bR and hindering the growth of the HBP. Once the value of r was less than 1, that is β1 > 3, the DPw decreased abruptly. For example, in the case of r = 1 at pA = pB = 0.99, the DPw and DPn were 171 and 6.6, respectively, which decreased to 10.9 and 3.9 at pA = 0.99 and β1 = 4, in which r = 0.857. At a high conversion, the DPw of the conversion became less sensitive to the conversion than the system with r > 1. This result suggested that the molecular weights of the HBPs are more easily manipulated and controlled with the addition of BR at β1 > 3. Figure 5 shows the number fractions of the residual monomers that are dependent on the value of β1 at λ2 = 3.

Figure 6. Profile of degree of polymerization dependent on the conversion at different ratios of BR at r = 1.

The DPw and polydispersity index (PDI) of the polymers were dependent on β1 near the full conversion at r = 1, as summarized in Figure 7. As shown in Figure 2, at β1= 2.5, the

Figure 5. Fractions of residual monomers dependent on the ratio of BR at λ2 = 3 and conversion of 0.95 or 0.99.

If β1 = 0 and r = 2, then group A was in excess. The number fraction of monomer A2, [A2], was 0.75 initially, and this value decreased to 0.21 at pB = 0.95 and pA = 0.475. Meanwhile, most of the monomers B3 had been consumed, of which [B3] was approximately 0.00003 at pB = 0.95. The residual monomer A2 could be further reduced by the addition of BR. In the case of β1 = 3 and r = 1, both of the initial [A2] and [BR] values were 0.43; these values decreased to 0.0011 and 0.021, respectively, at pB = pA = 0.95. If group B was in excess, r < 1, then the residual BR and B3 increased by adding more of the monofunctional compound BR. The initial composition of the monomers was under equal number groups of A and B (i.e., r = 1). According to Figure 2, along the line “vy” and β1 < 3, the gel is formed at the conversions of A and B less than 1, which implies that gelation could occur during polymerization. Figure 6 indicates the DPw of the polymers that were dependent on the conversion under various contents of BR at r = 1. At β1 = 0 and λ2= 1.5, the DPw increased with increasing conversion, and this value tended upward to infinite values at the critical conversions of A and B, approximately 0.71, which increased with an increasing ratio of BR to β1. At β1 = 3, the gel was formed at pB = pA = 1. If β1 > 3 and r = 1, that is, along the line “vu” in Figure 2, then all the A and B groups were totally consumed, and the value of DPw remained finite. For example, the DPw was approximately 53 at β1 = 3.2 and pB = pA = 1. Thus, HBPs without a gel fraction could be prepared at a high conversion by adding a certain amount of BR.

Figure 7. DPw and PDI of polymers dependent on the ratio of BR at r = 1 and conversion of 0.95, 0.99, or 0.999.

critical conversion was less than 0.95, and gelation would take place before the conversion of 0.95. If more end-capping molecules BR were added to the ratio β1= 2.5, then no gel formed at pB = pA = 0.95, and the DPw and PDI of the polymers were 101 and 17, respectively, which decreased with the addition of BR and reduced to 33.6 and 6.2 at β1 = 3, respectively. The critical conversion was 1 at β1 = 3; thus, the polymers could further grow to DPw = 171 at pA = 0.99 and 1710 at pA = 0.999. Once β1 > 3, the critical conversion was larger than 1. The DPw and PDI decreased quickly with an increase of β1 from 3 to 3.5 at a high conversion; then, these parameters decreased slightly with a higher content of BR. The results indicated that the polymerization could avoid gelation by adding a higher ratio of BR, and the distribution of the molecular weights of the polymers became narrower. However, the DP of the polymers decreased. The degree and fraction of branching of polymers, DB and FB, were calculated by the generating function method and eqs 12 and 13. Figure 8 shows the DB and FB that are dependent on β1 at a conversion of 0.99, and r = 1 or λ2 = 3. If β1 < 3 and λ2 = 3, the three functional monomers B3 were almost reacted at pB = 0.99. Therefore, the DB was approximately 0.97, which was very close to 1. Note that there were still a few trimers; Rbaa-bR would be produced as a mixture with the HBPs during 11767

DOI: 10.1021/acs.iecr.9b00351 Ind. Eng. Chem. Res. 2019, 58, 11763−11769

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Industrial & Engineering Chemistry Research

as β1 = 4 or 4.5. The result was consistent with the proposed model shown in Figure 4. At r = 1, by increasing the ratio of HEA, the molecular weight of the polymers decreased, but the fraction of trimer (Rb-aa-bR) increased. There were a few deviations between the experimental data and the calculated results, which might be caused by the simplified kinetic model, such as the equal reactivity of the functional groups, and no cyclization occurring before gelation, as well as the GPC calibration by using the linear polystyrene.

■

CONCLUSIONS The stepwise polymerization of a mixture of monomers A2 and B3 with end-capping molecules BR was studied by recursive and kinetic models. By utilizing the diagram of the sol and gel regions that are dependent on the initial molar ratios of A2 to B3 and BR to B3 (λ2 and β1), it is possible to prepare hyperbranched polymers without a gel fraction at a high conversion of the groups by adding BR into the reactor. The number- and weight-average degree of polymerization (DPn and DPw, respectively) as well as the fraction of branching of polymers can be manipulated by the initial composition of monomers. Polyurethane acrylates were further synthesized via the stepwise polymerization of trimethylolpropane ethoxylate, hexamethylene diisocyanate, and hydroxyethyl acrylate under an equal stoichiometric amount of groups A and B with r = 1. The number- and weight-average molecular weights of the PUAs determined by GPC were 1793 and 7670, respectively, and these values decreased with increasing BR. The trends were highly consistent with the theoretical model.

Figure 8. Degree and fraction of branching of polymers dependent on the ratio of BR at pA or pB = 0.99.

polymerization. The FB was 0.3 at β1 = 0 and then decreased gradually to 0.14 at β1 = 3. Subsequently, both DB and FB decreased with an increase in BR, but they were maintained at higher values for the system with an equal initial number of groups A and B, r = 1. Polyurethane acrylates (PUAs) with different molecular structures were synthesized via a stepwise polymerization of monomers B3, trimethylolpropane ethoxylate (TMPE, Aldrich), A2, hexamethylene diisocyanate (HDI, TCI), and BR, hydroxyethyl acrylate (HEA, TCI) in acetone with the addition of dibutyltin dilaurate (Aldrich) as the catalyst. The mixture at various ratios of isocyanate (A) and hydroxyl (B) groups reacted for 2−3 h at 30 °C. The molecular weights of the branched PUAs were determined by GPC coupled to two columns (SSI/Lab Alliance HPLC pump/RI 2000, PLgel mixed-C and PLgel 100 Å). Tetrahydrofuran was the carrier solvent, and the columns were calibrated with polystyrene standards. If β1 = 2 or 2.6, then gelation occurred in less than 1 h. When β1 increased to 3, the number- and weight-average molecular weights, Mn and Mw, of the polymers measured by GPC were 1793 and 7670, respectively, as shown in Table 2.

■

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.9b00351. Degree of polymerization of hyperbranched polymers calculated by generating the function method (PDF)

■

β1

pA

2.5 2.8 3 3 3 3.5 4 5 6

2 2.6 3 4 4.5 4 5 7 9

gel gel 0.95 0.98 0.99 0.98 0.98 0.99 0.98

Mw

Mn

AUTHOR INFORMATION

Corresponding Author

Table 2. Molecular Weights of the Polymers Measured by the GPCa λ2

ASSOCIATED CONTENT

*E-mail: [email protected]. ORCID

Rb-aa-bR (%)

Kuo-Chung Cheng: 0000-0002-1411-3167 Notes

7670 1595 1179 5328 4385 2212 1905

(9040) (2670) (2000) (4820) (2850) (1760) (1280)

1793 (999) 691 (668) 538 (576) 1377 (918) 1205 (789) 848 (677) 791 (590)

24 31 33 32 39 56 61

The authors declare no competing financial interest.

■

(21) (27) (29) (29) (35) (46) (52)

ACKNOWLEDGMENTS We thank the Ministry of Science and Technology of Taiwan for their financial support of this study under Contract No. MOST 106-2221-E-027-118.

■

a

Parentheses indicate calculation by the kinetic model.

REFERENCES

(1) Kim, Y. H. Hyperbranched Polymers 10 Years after. J. Polym. Sci., Part A: Polym. Chem. 1998, 36, 1685. (2) Gao, C.; Yan, D. Hyperbranched Polymers: from Synthesis to Applications. Prog. Polym. Sci. 2004, 29, 183. (3) Gretton-Watson, S.; Alpay, E.; Steinke, J.; Higgins, J. Hyperbranched Polymers. Synthesis, Modeling, Experimental Validation, and Rheology of HyperbranchedPoly(methyl methacrylate) Derived from a Multifunctional Monomer (MFM) Route. Ind. Eng. Chem. Res. 2005, 44, 8682. (4) Hult, A.; Johansson, M.; Malmstrom, E. Hyperbranched Polymers. Branched Polymers II; Springer: Berlin, 1999.

Meanwhile, the conversion of isocyanate groups was approximately 0.95, which was determined by the reduced intensity of absorption at 2272 cm−1 in the Fourier transform infrared spectrum. The fraction of the trimer formed by the one HDI and the two HEAs was 24%, which was estimated by the GPC data calibrated with the trimers prepared from HDI and HEA at a molar ratio of 1:2. The molecular weight of the polymers decreased with the addition of the excess HEA, such 11768

DOI: 10.1021/acs.iecr.9b00351 Ind. Eng. Chem. Res. 2019, 58, 11763−11769

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DOI: 10.1021/acs.iecr.9b00351 Ind. Eng. Chem. Res. 2019, 58, 11763−11769