Effect of surfactants on the swelling behaviors of thermosensitive hydrogels: applicability of the generalized Langmuir isotherm

Abstract

Herein, the surfactant effects on the thermosensitive swelling behaviors of nanometer-sized particle gels are investigated. N-Diethylacrylamide (NDEA) particle gels are prepared by precipitation polymerization with a neutral initiator (tert-butyl hydroperoxide (TBHPO)) to prevent neutralization of the anionic groups in the gel network by the ionic initiators with oppositely charged surfactants. A photon correlation spectroscopy (PCS) technique is utilized to detect the effect of ionic surfactants (sodium dodecyl sulfate (SDS) and dodecyltrimethylammonium bromide (DTAB)) on the thermosensitive swelling behaviors of the hydrogel. A thermodynamic framework for describing the surfactant effect on the swelling behavior of the hydrogel is established by applying the generalized Langmuir isotherm (GLI), which considers both the binding isotherm of the surfactant and the effect of the electrical double layer of the bound surfactant on the conventional thermodynamic model. For comparison, two lattice models, the modified double lattice temperature (MDL T) and modified Flory–Huggins (MFH) models, are employed as mixing contributions and the Flory–Rehner (FR) model is used as an elastic contribution. Experimental results show an obvious increase in both the volume phase transition temperature (VPTT) and the swelling ratio of hydrogels after adding surfactants. The calculation results show that the ability to describe the VPTT and swelling ratio of various hydrogels in surfactant solutions is significantly improved when the GLI is combined with the conventional thermodynamic model.

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Introduction

Hydrogels have been extensively investigated on account of their stimulus-sensitivity to a variety of external factors including temperature,^1,2 pH,^3–5 cosolvents,^6–8 cosolutes,^9–14 etc. Most non-ionic thermosensitive hydrogels are low critical solution temperature (LCST)-type hydrogels with amide groups such as poly(N-isopropylacrylamide) (PNIPA),^15–24 poly(N-isopropylmethacrylamide) (PNIPMA),^25–27 poly(N-vinylcaprolactam) (PNVCL),^13,28–30 and poly(N,N-diethylacrylamide) (PNDEA).^18,21,31,32

To control the thermosensitivity and swelling ability of a hydrogel, the addition of certain cosolutes (salts^9–11 and surfactants^13,14) is useful. Although adding salts to a gel network decreases both the VPTT and the swelling ability, the presence of bound surfactants on a gel network increases the VPTT and swelling ability due to electrostatic repulsion from the bound aggregates of the surfactant as depicted in Fig. 1. These characteristics are useful for some applications such as immobilization of enzymes,³³ controlled release of chemicals³⁴ and tissue engineering.³⁵

Fig. 1 Schematic representation of the effect of surfactant on thermosensitive hydrogel (assuming that an anionic surfactant is introduced) and chemical structures of the surfactant used in this work.

Since the pioneering work of Eliassaf,³⁶ numerous studies investigating surfactant binding on non-ionic polymers and gels have been conducted.^37–41 Some studies^38–41 have reported that bound ionic surfactants on gel interfaces generate electrostatic interactions and that non-ionic hydrogels exhibit similar characteristics to those of polyelectrolyte hydrogels. However, Kokufuta et al.^41,42 suggested that the volume phase transition of NIPA gels bound by ionic surfactants cannot be explained via the Donnan potential. Some researchers^43,44 have shown that the binding isotherm of SDS to PNIPA particle gels follows the Langmuir isotherm curve.

For a quantitative approach to study the swelling behaviors of hydrogels, various molecular thermodynamic models have been investigated. In these, modified forms of the Flory–Huggins theory^45–47 (as a mixing contribution) are combined with the rubber elasticity contribution using the Flory–Rehner^48,49 or Flory–Erman^50–52 chain models. The thermosensitive swelling behaviors of homogeneous gels in single solvents or cosolvents have been analyzed by many researchers.^53–57 Recently, thermodynamic models to describe the abnormal swelling behaviors of inhomogeneous gel, like core–shell gel networks, have been developed.^58–61 Lee and Bae^47,62 successfully described the cosolvency effects on the upper critical solution temperature (UCST)-type swelling behaviors of core–shell gel particles based on the MDL-T model. The influence of pH or salt on the swelling behaviors of hydrogels has been studied by introducing classical Donnan theory, which considers the charged substances and permeable ionic species that pass through a Donnan membrane.^63–65 There are various models that can be used to describe interactions between oppositely charged surfactants and polyelectrolytes^38,66–68 as well as binding isotherm models for surfactants on proteins, polymers or gels.^69–71 Alternatively, few attempts have been made to establish quantitative approaches for describing the swelling behavior of non-ionic hydrogels in a surfactant solution.

The present study investigates the effect of anionic (SDS) and cationic surfactants (DTAB), see Fig. 1, on the thermosensitive swelling behaviors of NDEA particle gels by using the PCS technique. A neutral initiator (TBHPO) is introduced to avoid neutralization between the oppositely charged initiator and surfactant.¹³ A new thermodynamic framework, which results from combining the GLI⁷² with the conventional thermodynamic model for the swelling behavior of hydrogel, accounts for the effects of the surfactant binding on the swelling behavior of the hydrogel. Three additional parameters for the GLI are also introduced: the specific interaction parameter of the bound surfactant (δ[small epsilon, Greek, tilde]_ij,s0), the Langmuir constant (K_L) accounting for the maximum amount of binding sites on the gel interface, and the electrostatic potential parameter (ψ_s). The general applicability of combining the GLI with conventional thermodynamic models (MDL T⁶² and MFH⁷³ models) along with the limited chain length (which is dependent on the parameters of the MDL base models) are examined simultaneously. The calculation results provide fairly accurate descriptions of the effect of surfactants on the thermosensitive swelling behaviors of hydrogels.

Experimental

Preparation of neutral NDEA particle gels

NDEA (monomer), N,N′-methylenebisacrylamide (BIS, cross-linker), SDS (anionic surfactant), DTAB (cationic surfactant), and TBHPO (neutral initiator) were used as received from Aldrich.

Neutral PNDEA particle gels were prepared by precipitation polymerization. The synthetic details using TBHPO neutral initiator follows the route described in a previous work.¹³ The monomer solution, which is composed of the NDEA monomer (0.2 g), the BIS crosslinker (0.01 g), SDS surfactant (0.01 g) and DI water (50 mL) was introduced into a Pyrex reactor equipped with a mechanical stirrer, a nitrogen gas stream, and a reflux condenser. The solution was mixed at 108 °C for 2 h. The reaction started upon the addition of an 80% TBHPO solution (0.13 g), and was carried out for 30 h. The prepared gel solution was filtered through a 0.45 μm syringe filter.

Field emission scanning electron microscope (FE-SEM)

The morphology of NDEA gels was characterized by a high resolution FE-SEM (Nova Nano SEM 450). The dispersion of particle gel on glass plate was dried in a vacuum oven at room temperature (28 °C) during 24 h.

The shapes of prepared gel particles show some difference with sphericity. The surface is somewhat rough than smooth. The diameters measured by SEM can be smaller than hydrodynamic size from DLS measurement, and the results represent 239–281 nm due to increased polydispersity of gels at swelling state.

Photon correlation spectroscopy (PCS) technique

To measure the hydrodynamic diameters of PNDEA particle gels, a Malvern Zetasizer Nano ZS equipped with a He–Ne laser (λ = 633 nm) at an angle of 173° was used. Dilute samples were measured in a Pyrex cuvette to avoid multiple scattering, and five measurement results were averaged at each temperature after an equilibrium time of 30 min. The diameters and polydispersity index (PDI) values were evaluated by Malvern Zetasizer Software ver. 7.11. The PDI value (less than 0.12) of n-NDEA particle gels indicates a uniform size distribution as shown in Fig. 3. As represented in Fig. 3(a), the z-average diameter at swollen state (28 °C) show similar size (273.5 nm) comparing with SEM images in Fig. 2.

Fig. 2 SEM images of n-PNDEA gels dried at room temperature (28 °C). (a) 258 nm, (b) 239 nm, and (c) 281 nm.

Fig. 3 Particle size distribution results at both collapsed and swollen states, as determined by the PCS technique. The measurement results of the NDEA particle gels in an (a) aqueous solution, (b) SDS (anionic surfactant) solution and (c) DTAB (cationic surfactant) solution.

The swelling ratio of the measured diameter data is determined by the volume ratio of the reference state gel as follows:

where D_h, V and ϕ_g are the hydrodynamic diameters, volume of the particle gel and volume fraction of the gel, respectively. The subscript “0” represents the reference state of the gel, which is a collapsed state over the LCST.

Model development

Generally, the electrostatic behavior of polyelectrolyte gels has been analyzed by combining Donnan theory with Flory–Huggins type equations. However, it was reported that identifying the electrostatic repulsion of bound surfactants with an osmotic effect by analyzing charged monomers and their counterions is inappropriate.^40–42 In this study, we propose a thermodynamic framework composed of a specific interaction and the interfacial contribution of the bound surfactant. When the surfactant molecules are adsorbed onto the gel, we then assumed the following on the basis of several experimental results.

(1) Polymer gels accept the hydrophobic tail of surfactant molecules on their hydrophobic elements, which form the aggregates replacing an interaction ability and an interfacial property of the screened hydrophobic elements.

(2) The adsorption isotherm of the surfactant molecules on the gel network follows the Langmuir monolayer isotherm.

(3) In view of the polymer chain, substituted hydrophilic elements from the surfactant aggregates critically disturb the interaction ability between the polymer gel and water, which increases the VPTT of the system.

(4) In view of the interface, monolayers composed of the ionic head group of bound surfactants cause the effects of the electrical double layer on the electrostatic and interfacial property of system.

The proposed net chemical potential of a water molecule becomes

Δμ_1,net = Δμ_1,mix + Δμ_1,ela + Δμ_1,inf (2)

where Δμ_1,mix is the chemical potential of the mixing contribution, Δμ_1,ela is the chemical potential of the elastic contribution and Δμ_1,inf is the chemical potential of the interfacial contribution, respectively.

Mixing contribution

Two lattice models are employed to consider the mixing contribution of the hydrogel system. However, each form of entropic and energetic contributions for free energy makes different quality of modeling results.

a. MDL T model^16,62,74,75. The Helmholtz free energy expression of the modified double lattice (MDL) model is written aswhere N_r is the total number of simple cubic lattice sites which have a coordination number z = 6; k is Boltzmann's constant; ϕ_i and r_i represent the volume fraction and the chain length parameter of component i, respectively; is the temperature dependent reduced interchange energy parameter between the i–j component.

The universal constants C_β and C_γ were determined to be 0.1415 and 1.7986, respectively, by fitting the Monte Carlo (MC) simulation data of small molecules.⁷⁴ Although there has been a lot of effort put into obtaining the universal constants in macromolecule systems (e.g., linear polymer systems^76–79), it is hard to correlate the universal constants with the simulation results of cross-linked polymer systems due to restricted simulation data of long-chain molecules. In addition, direct use of the universal constants for linear polymer systems has some limitations, and the analysis is presented in the ESI.† By simplifying the free energy expression, these problems are mathematically resolved by setting C_γ to 0 and C_β to 0.3. Influence of the universal constants is also presented in the ESI† by comparing the modeling results for the SDS/water/PNVCL gel systems.

The temperature-dependent interchange energy parameter ([small epsilon, Greek, tilde]_ij), which is mathematically optimized to the thermosensitive swelling behavior, is introduced by considering the enthalpic and entropic energy contributions as below:

where [small epsilon, Greek, tilde]_ij,weak and δ[small epsilon, Greek, tilde]_ij are the reduced interaction parameters of the ordinary and specific interaction, respectively; superscript H and S are the enthalpic and entropic contributions, respectively; and κ is the degeneracy parameter.

b. MFH model⁷³. The modified Flory–Huggins (MFH) model is given by

The chi (χ_ij) interaction parameter of the Flory–Huggins model was substituted with the reduced interchange energy parameter ([small epsilon, Greek, tilde]_ij) in order to account for the temperature dependence.

Oh and Bae⁷⁴ reported the secondary lattice concept, which accounts for the specific interactions between segments, from a mathematical approximation of the double lattice model. Each mixing contribution adopted the secondary lattice concept: this expression is represented as

where N_i,j is the number of i–j pairs; η (=0.3) is the surface fraction permitting oriented interactions; C_α (=0.4881) is a universal constant obtained from the MC simulation data of the Ising lattice; and δ[small epsilon, Greek, tilde]_ij (=δε_ij/kT) is the reduced oriented interaction. To incorporate the secondary lattice term, [small epsilon, Greek, tilde]_ij is replaced by if an oriented interaction occurs between the i–j segments.

Elastic contribution

The elastic contribution (i.e., a modified FR chain model) that was reported by Moerkerke et al.⁴⁹ iswhere are factors that depend on the volume fraction of the gel (ϕ_g); ϕ_g0 is the reference volume fraction of the gel; and m_c is the number of average lattice sites between the cross-linking sites. By assuming a perfect tetrafunctional network, the functionality of the cross-linker (f) is set to four.

Specific interaction of bound surfactant

Bound surfactants on the hydrophobic elements of the hydrogel become hydrophilic elements that specifically interact with adjacent water molecules. These substituted hydrophilic elements collapse the chain and make the network more extended, as shown in Fig. 4. As the limited binding sites are occupied with the added surfactant molecules, we assume that the interaction ability of the substituted hydrophobic elements of the hydrogel depend on the fraction of occupied binding sites. Adopting the classical Langmuir adsorption model^80–82 as the binding isotherm model, the fraction of occupied binding sites (θ) due to the added surfactants is presented below:where Γ is the concentration of the bound surfactant at the interface; Γ_∞ is the maximum possible concentration of the bound surfactant at the interface; c_surf is the concentration of the surfactant in the bulk solution; is a Langmuir constant related to the energy of binding per molecule; δ is the thickness of the binding layer; and μ^s₀ and μ₀ are the standard chemical potentials of the surfactant at the interface and in the bulk solution, respectively.

Fig. 4 Schematic representation of the substituted hydrophilic chain by binding surfactants on the network (assuming that an anionic surfactant is introduced).

Combining the Langmuir isotherm and the amount of specific interaction energy when all binding sites are substituted by surfactant aggregates, we then introduce a new specific interaction parameter for the bound surfactant–water pairs (δ[small epsilon, Greek, tilde]_s). This is composed of a surfactant concentration-dependent term θ(c_surf) and the reduced specific interaction energy of bound surfactants when all binding sites are occupied (δ[small epsilon, Greek, tilde]_ij,s0), as below:

δ[small epsilon, Greek, tilde]_ij,s = θ(c_surf) × δ[small epsilon, Greek, tilde]_ij,s0 (9)

The interchange energy parameter replaced by incorporating the specific interaction parameter of the bound surfactants (δ[small epsilon, Greek, tilde]_ij,s) is given by

[small epsilon, Greek, tilde]_ij = [small epsilon, Greek, tilde]_ij,gel + δ[small epsilon, Greek, tilde]_ij,s (10)

where [small epsilon, Greek, tilde]_ij,gel is the interchange energy parameter between i–j component in surfactant-free condition which is determined by mixing model.

Interfacial contribution

The interfacial contribution due to the bound surfactants is introduced by considering the double-layer resulting from the charge of the bound surfactant monolayer. A schematic representation of the electrical double layer between the gel and solvent phase is described in Fig. 5. Following the Gibbs adsorption equation, the decrement of the interfacial tension is described aswhere σ is the interfacial tension and Γ_i and c_i are the interface and bulk concentrations of the i-th surfactant, respectively.

Fig. 5 Schematic representation of electrical double layer between gel and solvent phase by binding surfactants on the network (assuming that an anionic surfactant is introduced).

Various interfacial double-layer theories have been developed since the Helmholtz model. Among these theories, the Gouy–Chapman double-layer theory⁸³ was generated by combination with the well-known Langmuir isotherm as described below.⁷²

where A1 is a constant related to the non-electrostatic interactions among the bound surfactants; Z is the valency of the surfactant; e is the elementary charge; and ψ_s represents the electric potential at the interface. In this study, for simplicity, we neglect the trivial non-electrostatic interactions of the bound surfactant (A1 = 0).

By integrating eqn (11), the generalized Langmuir isotherm (GLI, eqn (12)) is derived in terms of the osmotic pressure as

where ε is the dielectric constant of the solution and C is the total electrolyte concentration (surfactant + added salt).

Finally, the eqn (13) is converted to an expression that represents the chemical potential of the interfacial tension by using the relationship between the osmotic pressure and chemical potential, given as

Δμ_inf = −v_solvπ_inf (14)

where v_solv is the molar volume of the solvent. By generalized Langmuir isotherm theory, the electrostatic interaction at the gel–solvent interface is considered from the viewpoint of chemical potential.

Equilibrium calculation

To determine the equilibrium conditions of the swelling behavior, the net chemical potentials of the solvent between the gel phase and the solvent phase should be equal:

Δμ^gel_1,net = Δμ^solv_1,net (15)

where the superscripts “gel” and “solvent” indicate the inner gel phase and the outer solvent phase, respectively. The mixing and elastic chemical potentials are calculated by differentiating the change in the Helmholtz free energy by the number of molecules (N_i).

Results and discussion

Thermodynamic modeling

Before solving the equilibrium calculation, the predetermined model parameters should be clarified. List of system and predetermined network parameters is represented in Table 1. We assume that all systems are water/polymer gel binary systems, and set water as component 1 and reference molecule (r₁ = 1). In the case of the polymer gel, the chain length of the cross-linked network is considered to be infinite (r₃ = ∞). The reference state of the gel is assumed to be a completely collapsed state, indicating that the value of ϕ_g0 is 1. The average number of lattice sites between the cross-linking sites is obtained from experimental conditions, as described below:where V_w,monomer and V_w,solvent are the Bondi's van der Waals volumes of the monomer of gel and solvent, respectively. Among the model parameters of the GLI, we assume and δ = 10 nm. K_L is used as an adjustable model parameter that modulates the capacity of surfactant binding per volume.

Table 1 List of system and predetermined network parameters

Systems	Network parameters
	ϕg0	mc
SDS/water (1)/PNVCL gel (2)^13	1	136.6
SDS/water (1)/PNIPA gel (2)^84	1	277.92
SDS/water (1)/n-PNDEA gel (2)	1	75.127
DTAB/water (1)/n-PNDEA gel (2)

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The description for the swelling equilibrium of a hydrogel in a surfactant solution is significantly improved by applying the GLI to the conventional thermodynamic model. We examine a new model for an SDS/water (1)/PNVCL gel (2) system. The thermosensitive swelling behaviors of the PNVCL hydrogel in an aqueous surfactant-free solution are shown in Fig. 6(a). Adjustable model parameters for the given mixing models are determined by fitting the experimental results as a consequence of the equilibrium calculation (case I, Table 2). As depicted in Fig. 6(b), the increase in the VPTT of PNVCL gel in an SDS surfactant solution is appropriately described. The specific interaction parameter of the bound surfactant–water pair (δ[small epsilon, Greek, tilde]_12,s0) and Langmuir constant (K_L) are introduced (case II, Table 3). With increasing K_L, the fraction of occupied binding sites (θ(c_surf)) tends to decrease at the same surfactant concentration. In addition, the influence of δ[small epsilon, Greek, tilde]_12,s0 varies depending on the binding isotherm results (see the ESI†). The same K_L values are used regardless of the mixing models, in that the probability of the binding is equal in same systems. By supplementing the electrostatic effect of the ionic species on the gel interface, the electric potential at the interface (ψ_s) is determined from previously obtained model parameters (case III, Table 3). By considering the electrostatic energy of the binding surfactant, it was observed that the chemical potential of the solvent is decreased compared to case II (see the ESI†). In Fig. 6(c), the calculated results show a marked improvement, especially in the swollen state. The calculation procedure is presented in the ESI† for cases I through III.

Fig. 6 Experimental and modeling results of the thermosensitive swelling behavior of the PNVCL gel in surfactant solution for (a) case I, (b) case II and (c) case III. Dots and lines represent experimental results and modeling results, respectively.

Table 2 List of system and model parameters in case I

Systems	Model	ε12/k		δε12/k		κ
		ε^H12/k	ε^S12/k	δε^H12/k	δε^S12/k
SDS/water (1)/PNVCL gel (2)^13	MDL T	46 890.9	144.6	−49 997.0	−155.0	0.00026
	MFH	1736.3		−1647.8		—
SDS/water (1)/PNIPA gel (2)^84	MDL T	2633.50	7.985	−8070.15	−25.89	0.19531
	MFH	2258.0		−1867.2		—
SDS/water (1)/n-PNDEA gel (2)	MDL T	8169.50	25.18	−18 538.7	−59.52	0.0086
DTAB/water (1)/n-PNDEA gel (2)	MFH	2854.2		−2026.3		—

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Table 3 List of system and model parameters in case II and III

Systems	Model	Mixing parameters	Interfacial tension parameters
		δ[small epsilon, Greek, tilde]12,s0^a	KL^a	ψs^b
a Model parameters determined from case II.b Model parameters determined from case III.
SDS/water (1)/PNVCL gel (2)^13	MDL T	−10.88	0.12	−149.5
	MFH	−28.94		−137.9
SDS/water (1)/PNIPA gel (2)^84	MDL T	−19.91	0.10	−86.17
	MFH	−16.95		−94.78
SDS/water (1)/n-PNDEA gel (2)	MDL T	−82.09	0.20	−129.2
	MFH	−89.30		−181.0
DTAB/water (1)/n-PNDEA gel (2)	MDL T	−15.46	0.03	+176.6
	MFH	−9.345		+198.2

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To verify the validity of the proposed model, we report other three hydrogel systems in surfactant solutions with their modeling results. In Fig. 7, the calculation results of three models are compared with the experimental results of PNIPA gel with various SDS concentrations. The effect of SDS on the swelling results of the PNIPA gel is different from that of the PNVCL gel. Depending on the binding capacity of each polymer, the same surfactant affects the phase equilibrium differently. The increase in the VPTT of PNIPA gel is less than that of the PNVCL gel in the same SDS solution. In this system, mismatch of the binding isotherm model with the experimental results is represented by the deviation of VPTT for the SDS 1.40 mM solution. Different from the other hydrogel systems presented in this work, the PNIPA particle gel is prepared via a slightly ionic initiator,⁸⁴ which may result in a non-Langmuir binding isotherm.

Fig. 7 Experimental results of the thermosensitive swelling behavior of the PNIPA gel in an SDS solution and the modeling results: (a) case I, (b) case II, and (c) case III. Dots and lines represent experimental results and modeling results, respectively.

Thermosensitive swelling behaviors of neutral PNDEA gel in SDS and DTAB surfactant solutions are represented in Fig. 8, respectively. In this study, gel particles are prepared with a neutral initiator (TBHPO), which inhibits neutralization between the oppositely charged surfactants and gel particles. Neutral gel particles show good swelling behavior results in both anionic and cationic surfactant solutions; this result is expected. Electric potentials at the interface (ψ_s) for the cationic surfactants (DTAB) give positive values, as listed in Table 3. Overall, the descriptions for the swelling behaviors in surfactant solutions correspond well with the experimental data as shown in Fig. 8. However, the calculated results from the MDL T and MFH models are slightly underestimated compared with the experimental data in the high-concentration SDS solution, as shown in Fig. 8(c). By lowering the temperature below the LCST of the n-PNDEA gel in the 3 mM SDS solution, the gel network swells more abruptly than for the lower concentration solutions. Because the trend of temperature-dependence for the modeling results does not vary when using this method, experimental results at high concentrations are hard to describe. Some reports have suggested that the micelles of surfactant molecules cause a steric effect or repulsion with the network, which may promote swelling of the network.

Fig. 8 Experimental results of the thermosensitive swelling behavior of the n-PNDEA gel: (a) case I in surfactant free solution; (b) case II and (c) case III in SDS solution; and (d) case II and (e) case III in DTAB solution, respectively.

Significances and limitations

The swelling behaviors of thermosensitive hydrogels are significantly influenced by surfactant binding at the interface of the hydrogel. The neutral particle gels prepared in this work illuminate the additive effect of both anionic and cationic surfactants in an aqueous medium. There are significant limitations to the base lattice models. First, the cosolutes (e.g., salts, surfactants, or ionic liquids) have a much greater effect on the swelling behaviors of gels compared to the effects of the cosolvents. At the beginning of model development, the lattice model excludes various electrostatic interactions. Second, limitation of the maximum swelling ratio by the MDL base model restricts its ability to accurately describe the swelling behaviors of homopolymer gel systems (see the ESI†). By overcoming the limitation of the conventional gel swelling models, meaningful descriptions of the thermosensitive swelling behavior in surfactant solutions are accomplished by combining the binding isotherm model (generalized Langmuir isotherm, GLI) with lattice-based thermodynamic models. The fraction of occupied binding sites (θ(c_surf)), which reflects the well-known Langmuir binding isotherm of the surfactant, moderately complements the increase in the VPTT caused by the bound surfactant. In addition, electrostatic interactions of bound surfactants were considered by the Gouy–Chapman double-layer theory of GLI, and the swollen state was successfully described.

However, the inaccuracy of the simple isotherm model is obvious. Temperature dependence of the binding and the electrical potential of the double layer should be handled more elaborately. In addition, the salting-out effect, which occurs if the surfactant concentration is significantly increased, cannot be reproduced using this modeling method. With respect to the isotherm model considering the amount of bound surfactants, analytical theory for the salting-out effect should be introduced into the framework of the model. These topics are worthy of further investigation in our future works.

Conclusions

In this study, we suggested the applicability of the GLI to reproduce the swelling behaviors of hydrogels in surfactant solutions. The significance of this approach is that it includes the interaction of surfactants bound onto the gel surface as well as the amount of bounded surfactant molecules. We point out that the electrostatic repulsion and specific interactions caused by the bound surfactant result in an increase in both the VPTT and the swelling ability of the hydrogel systems. By adding three additional parameters (δ[small epsilon, Greek, tilde]_12,s0, K_L and ψ_s) to the conventional thermodynamic model for the swelling behaviors, combination of the given lattice models with the GLI successfully describes the interactions attributed to the bound surfactant. Furthermore, experimental studies investigating the influence of anionic and cationic surfactants on the thermosensitive swelling behaviors of neutral NDEA particle gels are reported using PCS technique. We expect that this quantitative approach will facilitates greater understanding of the swelling behaviors of hydrogels in various types of surfactant solutions.

Acknowledgements

This research was supported by (1) Global Ph.D Fellowship Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015H1A2A1034513), (2) Engineering Development Research Center (EDRC) funded by the Ministry of Trade, Industry & Energy (MOTIE) (No. N0000990).

References

1. V. Boyko, S. Richter, A. Pich and K.-F. Arndt, Colloid Polym. Sci., 2003, 282, 127–132.
2. R. F. Freitas and E. Cussler, Chem. Eng. Sci., 1987, 42, 97–103.
3. X. Gao, Y. Cao, X. Song, Z. Zhang, C. Xiao, C. He and X. Chen, J. Mater. Chem. B, 2013, 1, 5578–5587.
4. A. Fernandez-Nieves, A. Fernández-Barbero, B. Vincent and F. De las Nieves, Macromolecules, 2000, 33, 2114–2118.
5. H. Bysell, A. Schmidtchen and M. Malmsten, Biomacromolecules, 2009, 10, 2162–2168.
6. N. Orakdogen and O. Okay, Polymer, 2006, 47, 561–568.
7. C. Scherzinger, A. Schwarz, A. Bardow, K. Leonhard and W. Richtering, Curr. Opin. Colloid Interface Sci., 2014, 19, 84–94.
8. T. Amiya, Y. Hirokawa, Y. Hirose, Y. Li and T. Tanaka, J. Chem. Phys., 1987, 86, 2375–2379.
9. C. H. Lee and Y. C. Bae, Macromolecules, 2015, 48, 4063–4072.
10. S. Beltran, H. H. Hooper, H. W. Blanch and J. M. Prausnitz, J. Chem. Phys., 1990, 92, 2061.
11. M. Annaka, K. Motokawa, S. Sasaki, T. Nakahira, H. Kawasaki, H. Maeda, Y. Amo and Y. Tominaga, J. Chem. Phys., 2000, 113, 5980.
12. C. S. Renamayor, A. Pastoriza, C. L. Usma and I. F. Pierola, Colloid Polym. Sci., 2013, 291, 2017–2021.
13. Y. Gao, S. C. Au-Yeung and C. Wu, Macromolecules, 1999, 32, 3674–3677.
14. N. Wada, Y. Kajima, Y. Yagi, H. Inomata and S. Saito, Langmuir, 1993, 9, 46–49.
15. S. M. Kim and Y. C. Bae, Polymer, 2013, 54, 2138–2145.
16. S. Y. Oh, H. J. Kim and Y. C. Bae, Polymer, 2013, 54, 6776–6784.
17. S. Gallagher, A. Kavanagh, B. Ziolkowski, L. Florea, D. R. MacFarlane, K. Fraser and D. Diamond, Phys. Chem. Chem. Phys., 2014, 16, 3610–3616.
18. C. Scherzinger, P. Lindner, M. Keerl and W. Richtering, Macromolecules, 2010, 43, 6829–6833.
19. K. Otake, H. Inomata, M. Konno and S. Saito, Macromolecules, 1990, 23, 283–289.
20. H. Kawasaki, S. Sasaki and H. Maeda, J. Phys. Chem. B, 1997, 101, 4184–4187.
21. L. Patra, A. Vidyasagar and R. Toomey, Soft Matter, 2011, 7, 6061.
22. T. G. Park and A. S. Hoffman, Macromolecules, 1993, 26, 5045–5048.
23. A. Lele, M. Hirve, M. Badiger and R. Mashelkar, Macromolecules, 1997, 30, 157–159.
24. X.-Z. Zhang and R.-X. Zhuo, Langmuir, 2001, 17, 12–16.
25. K. von Nessen, M. Karg and T. Hellweg, Polymer, 2013, 54, 5499–5510.
26. X. Hu, Z. Tong and L. A. Lyon, Colloid Polym. Sci., 2010, 289, 333–339.
27. I. Berndt, J. S. Pedersen, P. Lindner and W. Richtering, Langmuir, 2006, 22, 459–468.
28. A. Imaz and J. Forcada, J. Polym. Sci., Part A: Polym. Chem., 2011, 49, 3218–3227.
29. A. Laukkanen, S. Wiedmer, S. Varjo, M.-L. Riekkola and H. Tenhu, Colloid Polym. Sci., 2002, 280, 65–70.
30. L. M. Mikheeva, N. V. Grinberg, A. Y. Mashkevich, V. Y. Grinberg, L. T. M. Thanh, E. E. Makhaeva and A. R. Khokhlov, Macromolecules, 1997, 30, 2693–2699.
31. Y. Maeda, H. Yamamoto and I. Ikeda, Colloid Polym. Sci., 2004, 282, 1268–1273.
32. M. Colonne, Y. Chen, K. Wu, S. Freiberg, S. Giasson and X. Zhu, Bioconjugate Chem., 2007, 18, 999–1003.
33. T. G. Park and A. S. Hoffman, Appl. Biochem. Biotechnol., 1988, 19, 1–9.
34. A. S. Huffman, A. Afrassiabi and L. C. Dong, J. Controlled Release, 1986, 4, 213–222.
35. H. Weng, J. Zhou, L. Tang and Z. Hu, J. Biomater. Sci., Polym. Ed., 2004, 15, 1167–1180.
36. J. Eliassaf, J. Appl. Polym. Sci., 1978, 22, 873–874.
37. R. Mészáros, I. Varga and T. Gilányi, J. Phys. Chem. B, 2005, 109, 13538–13544.
38. A. M. Rumyantsev, S. Santer and E. Y. Kramarenko, Macromolecules, 2014, 47, 5388–5399.
39. S. Peng and C. Wu, Macromolecules, 2001, 34, 568–571.
40. E. Kokufuta, Y. Q. Zhang, T. Tanaka and A. Mamada, Macromolecules, 1993, 26, 1053–1059.
41. E. Kokufuta, H. Suzuki and D. Sakamoto, Langmuir, 1997, 13, 2627–2632.
42. H. Suzuki and E. Kokufuta, Colloids Surf., A, 1999, 147, 233–240.
43. E. Abuin, A. Leon, E. Lissi and J. Varas, Colloids Surf., A, 1999, 147, 55–65.
44. S. Mears, Y. Deng, T. Cosgrove and R. Pelton, Langmuir, 1997, 13, 1901–1906.
45. M. Marchetti, S. Prager and E. Cussler, Macromolecules, 1990, 23, 3445–3450.
46. D. Zhi, Y. Huang, X. Han, H. Liu and Y. Hu, Chem. Eng. Sci., 2010, 65, 3223–3230.
47. S. M. Lee and Y. C. Bae, Soft Matter, 2015, 11, 3936–3945.
48. P. J. Flory and J. Rehner Jr, J. Chem. Phys., 1943, 11, 521–526.
49. R. Moerkerke, R. Koningsveld, H. Berghmans, K. Dusek and K. Solc, Macromolecules, 1995, 28, 1103–1107.
50. P. Flory, J. Chem. Phys., 1977, 66, 5720–5729.
51. B. Erman and P. J. Flory, J. Chem. Phys., 1978, 68, 5363–5369.
52. P. J. Flory and B. Erman, Macromolecules, 1982, 15, 800–806.
53. K. Mukae, M. Sakurai, S. Sawamura, K. Makino, S. W. Kim, I. Ueda and K. Shirahama, J. Phys. Chem., 1993, 97, 737–741.
54. A. Hüther, X. Xu and G. Maurer, Fluid Phase Equilib., 2004, 219, 231–244.
55. Y. G. Kim, C. H. Lee and Y. C. Bae, Fluid Phase Equilib., 2014, 361, 200–207.
56. S. M. Kim and Y. C. Bae, Polymer, 2013, 54, 2138–2145.
57. G. Gürdağ and S. Çavuş, Polym. Adv. Technol., 2006, 17, 878–883.
58. C. Lian, D. Zhi, S. Xu, H. Liu and Y. Hu, J. Colloid Interface Sci., 2013, 406, 148–153.
59. J. Gernandt, G. Frenning, W. Richtering and P. Hansson, Soft Matter, 2011, 7, 10327–10338.
60. W. Hong, X. Zhao, J. Zhou and Z. Suo, J. Mech. Phys. Solids, 2008, 56, 1779–1793.
61. K. Sekimoto and K. Kawasaki, Phys. A, 1989, 154, 384–420.
62. S. M. Lee and Y. C. Bae, Macromolecules, 2014, 47, 8394–8403.
63. J. Ricka and T. Tanaka, Macromolecules, 1984, 17, 2916–2921.
64. P. K. Jha, J. W. Zwanikken and M. Olvera de la Cruz, Soft Matter, 2012, 8, 9519.
65. A. Khokhlov and K. Khachaturian, Polymer, 1982, 23, 1742–1750.
66. P. Kralchevsky, K. Danov, G. Broze and A. Mehreteab, Langmuir, 1999, 15, 2351–2365.
67. A. R. Khokhlov, E. Y. Kramarenko, E. E. Makhaeva and S. G. Starodubtzev, Macromol. Theory Simul., 1992, 1, 105–118.
68. P. Hansson, Langmuir, 1998, 14, 2269–2277.
69. C. Kotsmar, V. Pradines, V. Alahverdjieva, E. Aksenenko, V. Fainerman, V. Kovalchuk, J. Krägel, M. Leser, B. Noskov and R. Miller, Adv. Colloid Interface Sci., 2009, 150, 41–54.
70. O. Hamdaoui and E. Naffrechoux, J. Hazard. Mater., 2007, 147, 401–411.
71. O. Hamdaoui and E. Naffrechoux, J. Hazard. Mater., 2007, 147, 381–394.
72. R. Borwankar and D. Wasan, Chem. Eng. Sci., 1988, 43, 1323–1337.
73. J. G. Jung and Y. C. Bae, J. Polym. Sci., Part B: Polym. Phys., 2010, 48, 162–167.
74. J. S. Oh and Y. C. Bae, Polymer, 1998, 39, 1149–1154.
75. S. Y. Oh and Y. C. Bae, Eur. Polym. J., 2010, 46, 1860–1865.
76. S. K. Ryu and Y. C. Bae, Polymer, 2012, 53, 1339–1346.
77. J. G. Jung and Y. C. Bae, Eur. Polym. J., 2010, 46, 238–245.
78. B. H. Chang, K.-O. Ryu and Y. C. Bae, Polymer, 1998, 39, 1735–1739.
79. J. Yang, Q. Yan, H. Liu and Y. Hu, Polymer, 2006, 47, 5187–5195.
80. I. Langmuir, J. Am. Chem. Soc., 1917, 39, 1848–1906.
81. I. Langmuir, J. Am. Chem. Soc., 1916, 38, 2221–2295.
82. I. Langmuir, J. Am. Chem. Soc., 1918, 40, 1361–1403.
83. E. J. W. Verwey, J. T. G. Overbeek and J. T. G. Overbeek, Theory of the stability of lyophobic colloids, Courier Corporation, 1999.
84. C. Wu and Z. Shulqln, J. Polym. Sci., Part B: Polym. Phys., 1996, 34, 1597–1604.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra19696a

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