Ion transport in silicone hydrogel contact lenses

Journal of Membrane Science 399–400 (2012) 95–105

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Ion transport in silicone hydrogel contact lenses Cheng-Chun Peng, Anuj Chauhan ∗ Department of Chemical Engineering, University of Florida, Gainesville, FL 32611-6005, United States

a r t i c l e

i n f o

Article history: Received 11 July 2011 Received in revised form 24 January 2012 Accepted 27 January 2012 Available online 7 February 2012 Keywords: Ion permeability Silicone hydrogels Contact lens

a b s t r a c t Transport of ions through contact lenses is essential to maintain lens movement on the eye. We measure the effective diffusivity and partition coefficient of sodium chloride through silicone hydrogels by measuring kinetics of salt release and permeation in a diffusion cell. The results obtained from both approaches are compared and mechanisms related to linearity of transport and dominant transport mechanisms are explored. Also, transport parameters are measured from silicone hydrogels of several compositions to explore the dependency of ion transport on composition. Transport parameters are also correlated with the water fraction in the gel in the context of the free volume theory. Results show that the transport is linear in concentration and satisfies diffusive scaling suggesting that the transport of sodium and chloride ions can be lumped into an effective diffusion model. The permeation approach which is typically used for determining only the permeability can be utilized to yield both effective salt diffusivity and the partition coefficients if the short time transient data is fitted to a diffusion model. The values of diffusivity and partition coefficient obtained from both kinetic and permeation approach are comparable. The partition coefficient changes smoothly with variations in composition but there are discontinuities observed in diffusivity values likely due to changes in microstructure from dispersed to bicontinuous. The diffusivity cannot be related to the water content through the classical free volume theory because of the variations in the microstructure of the gels. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Contact lenses for correcting vision are available in several different wear-modalities including extended continuous wear for a period of 1–4 weeks, depending on the type of the lens. Extended wear lenses are required to allow rapid oxygen transfer because cornea is an avascular organ, and so it gets its oxygen supply directly from air [1,2]. Silicone based materials were explored as potential candidates for achieving the high oxygen transport due to the very high oxygen solubility in these materials. However, silicone based contact lenses were not useful as contact lens materials because the lenses made of such materials adhered to the cornea. It may be speculated that the hydrophobic nature of the silicone lenses leads to the adherence. It was however determined that surface treatment of a lens to render the surface hydrophilic is not enough to prevent lens adherence to cornea. If a particular lens material did not move on the eye, application to the surface of contact lens did not change the outcome significantly [3]. It was later discovered that the extended wear contact lenses are required to also allow sufficient ion transport to maintain on-eye movement and

∗ Corresponding author. Tel.: +1 352 392 2592; fax: +1 352 392 9513. E-mail address: [email protected]fl.edu (A. Chauhan). 0376-7388/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2012.01.039

not adhere to the cornea. The importance of ion permeability of contact lens material for maintaining lens motion was first described by Domschke et al. [4]. The need of ion transport through the lens is attributed to the requirement of a fluid hydrodynamic boundary layer between the lens and the cornea [5]. In the absence of the fluid layer, the lens can adhere to the cornea. Nicolson et al. claimed in an US patent that the ionoflux diffusion coefficient (Dion ), i.e., the ion permeability of the silicone hydrogel material, should be at least larger than 1.5 × 10−6 mm2 /min for sufficient on-eye movement of lens [6]. While ion permeability is critical to lens motion, an increase in the permeability beyond a critical value does not lead to a further increase in on eye movement of the lens [3]. To obtain high ion and oxygen permeabilities in contact lenses, hydrophilic monomers are copolymerized along with the hydrophobic siloxane monomers. In general, the polysiloxanes and the hydrophilic polymers are immiscible and thus a suitable macromer is needed in the monomer mixture to ensure solubilization of all monomers. The polymerized silicone hydrogel matrix can be best described as isotropic material with a dispersed microstructure with only one continuous phase or as an interpenetrating polymer network in which both the hydrophilic and hydrophobic phases are continuous throughout the material. A number of the commercial extended wear contact lenses are reported to possess a bicontinuous microstructure that facilitates rapid exchange of oxygen through the silicone rich phase and ions through the

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hydrophilic phase [3]. Thus, fine tuning of each composition in the hydrogel mixture with proper microstructure is critical to ensure the balance of all the key properties of the extended wear contact lenses, including oxygen permeability, ion permeability, water content, elastic modulus, surface wettability, etc. While the importance of ion permeability has been known for extended wear contact lenses, there are a very limited number of studies focusing on ion transport through the silicone hydrogels. Most prior studies on ion transport in contact lenses have reported the ion permeability, i.e., the product of the diffusivity and the partition coefficient, measured by direct permeation approach in a diffusion cell [3,6–10]. While ion permeability is important because it directly determines the net ion flux across the lenses at pseudo steady state, independent measurements of the diffusivity and partition coefficient are important as well because these two relate to different aspects of the lenses. Since partition coefficient is a thermodynamic property, it likely depends only on the total fraction of the two phases (silicone and hydrophilic) in the hydrogel matrix, while the diffusivity depends strongly on the connectivity of these phases (dispersed or bicontinuous morphology). Recently, Guan et al. reported measurements of both partition coefficients and diffusivity of sodium chloride in several commercial contact lenses [11]. These measurements were reported for various commercial contact lenses, which are available only in fixed compositions, and so it was not feasible to explore the effect of composition on transport parameters which are the focus of this paper. Also, Guan et al. utilized only the pseudo steady regime in the diffusion cell to determine the permeability, while we also explore the unsteady short time regime to determine both diffusivity and partition coefficient from the diffusion cell data. The diffusion of solutes in conventional hydrogels has been widely studied due to the its relevance in several application, including separation process such as chromatography [12], water purification [13–15], and hemodialysis [16,17]. Salt transport in hydrogels is typically explored through direct membrane permeation and kinetic sorption/desorption methods. In the direct membrane permeation approach, the permeability of a solute is calculated based on the measured permeation flux [13,18–24]. In the sorption/desorption experiments, the overall sorption or desorption kinetics are analyzed to characterize the diffusion coefficients of the solutes in the hydrogel [13,14,20–22,24,25]. Both models rely on ideal Fick’s law of diffusion to extract the transport parameters, and thus is suitable for homogeneous hydrogel systems where the transport of solute is controlled by self-diffusion [26]. In both approaches, simplified models based on short time release (kinetic sorption/desorption) or the pseudo steady state ion flux (direct permeation) are typically used to obtain the transport parameters. There are a number of models describing the diffusion of solutes in hydrogels, and an overview of these models and experimental data is available elsewhere [27]. One of the most popularly model for sodium chloride transport in hydrated homogenous hydrogels was first proposed by Yasuda et al. [21]. The model is based on the free volume theory by Cohen and Turnbull which is applicable to the process of solute diffusion in a pure liquid composed of hard molecular spheres [28]. Cohen and Turnbull derived the relation between the diffusion constant D in a liquid of hard spheres and the free volume as D = A exp(−v*/vf ), where vf is the free volume, v* is the minimum required volume of the void in which the solute can partition; A is a constant that is related to the average thermal velocity and the solute diameter, and  is a numerical factor used to correct for overlap of free volume available to more than one molecule [27,28]. Yasuda et al. applied the free volume theory to hydrated hydrogel systems to predict that the salt diffusion coefficient D in the hydrogel should be exponentially proportional to the reciprocal water fraction of the hydrated hydrogel. While this free volume theory model has successfully described the sodium chloride transport

in a variety of homogeneous hydrogels [13,14,18–21], the applicability of the free volume theory for salt transport in the silicone hydrogels has not been explored except for the recent study by Guan et al. [11]. In this study, we use both permeation measurement and kinetic sorption/desorption approach to explore sodium chloride transport in a variety of silicone hydrogel contact lens materials. The kinetic approach is utilized to measure both partition coefficient and the diffusivity [7,10,29,30]. The permeation approach is typically utilized for measuring only the permeability of the gel through pseudo-steady modeling of transport. Here, we propose to model the early transients before pseudo-steady state is achieved to determine both diffusivity and the partition coefficient of the materials. Results are compared from both approaches, i.e., diffusion cell and release in perfect sink. Also, fundamental issues related to mechanisms of transport are addressed and the dependence of the partition coefficient and the diffusivity on composition and microstructure are explored. 2. Materials and methods 2.1. Materials Ethylene glycol dimethacrylate (EGDMA, 98%), N,Ndimethylacrylamide (DMA, 99%) and 1-vinyl-2 pyrrolidone (NVP, 99+%) were purchased from Sigma–Aldrich Chemicals (Milwaukee, WI). Ethanol (99.5+%) and Dulbecco’s phosphate buffered saline (PBS) were obtained from Sigma–Aldrich Chemicals (St. Louis, MO). Sodium chloride (NaCl, 99.9+%) were purchased from Fisher Chemical (Fairlawn, NJ). The macromer acryloxy terminated ethyleneoxide dimethylsiloxane-ethyleneoxide ABA block copolymer, 80–120 cSt (DBE-U12, 95+%) were purchased from Gelest Inc. (Morrisville, PA). Methacrylic acid (MAA, 99.5%) were obtained from Polysciences, Inc. (Warrington, PA) and 3-methacryloxypropyltris(trimethylsiloxy)silane (TRIS) was supplied by Silar laboratories (Scotia, NY). 2,4,6-Trimethylbenzoyldiphenyl-phosphineoxide (Darocur® TPO) were kindly gifted by Ciba Specialty Chemicals (Tarrytown, NY), respectively. All chemicals were used without further purification. 2.2. Preparation of silicone hydrogel The silicone hydrogels were prepared by polymerizing a mixture of TRIS (silicone monomer); DMA and MAA (hydrophilic monomers); DBE-U12 (macromer); EGDMA (crosslinker) and NVP (hydrophilic additive) in various ratios listed in Table 1. The compositions in Table 1 can be classified into four categories. In Series A the ratio of DMA to MAA was varied while keeping the fraction of hydrophilic monomers (DMA + MAA) fixed; in series B the ratio of TRIS to macromer was varied while keeping the fraction of silicone component (TRIS + macromer) fixed; in series C the amount of crosslinker was varied while keeping amount of all other components fixed, and finally in Series D the composition was randomly chosen. As an example, to prepare Gel A1, 2.4 ml of a mixture that comprised 0.8 ml TRIS, 0.8 ml macromer and 0.8 ml of DMA was combined with 0.12 ml of NVP and 0.1 ml of EGDMA. The mixture was then purged with nitrogen for 15 min to reduce the dissolved oxygen. Next, 12 mg of photoinitiator Darocur® TPO was added with stirring for 5 min and the mixture was immediately injected into a mold. The mold comprised of glass plates separated by a plastic spacer of a desired thickness (0.13, 0.26 mm or 0.40 mm thick). The mold was then placed on Ultraviolet transilluminator UVB-10 (UltraLum Inc.) and the gel mixture was cured by irradiating with UVB light (305 nm) for 50 min. The synthesized hydrogel was either cut into circular pieces (about 1.65 cm diameter) with a cork borer

C.-C. Peng, A. Chauhan / Journal of Membrane Science 399–400 (2012) 95–105 Table 1 Composition of the silicone hydrogels. Each listed composition was mixed with additional 0.12 ml of NVP before polymerization. Sample

TRIS (ml)

Macromer (ml)

DMA (ml)

MAA (ml)

EGDMA (␮l)

A1/B1/C1 A2 A3 A4

0.80 0.80 0.80 0.80

0.80 0.80 0.80 0.80

0.80 0.68 0.56 0.40

– 0.12 0.24 0.40

100 100 100 100

B2 B3 B4 B5

1.20 1.00 0.60 0.40

0.40 0.60 1.00 1.20

0.80 0.80 0.80 0.80

– – – –

100 100 100 100

C2 C3 C4 C5 C6 C7

0.80 0.80 0.80 0.80 0.80 0.80

0.80 0.80 0.80 0.80 0.80 0.80

0.80 0.80 0.80 0.80 0.80 0.80

– – – – – –

10 30 50 75 300 500

D1 D2 D3 D4 D5 D6

1.37 1.37 0.60 0.48 0.96 0.40

0.34 0.69 0.60 0.48 0.48 0.40

0.69 0.34 1.20 1.44 0.96 1.60

– – – – – –

100 100 100 100 100 100

Below we first compare the transport measurements from the two different methods and then discuss the dependency of the transport parameters on composition. The two methods are compared only for Gels A3, and then the composition dependency of transport parameters measured through the kinetic approach is discussed for all the gels prepared. It is noted that the terms ion and salt diffusivity are used interchangeably in this paper. The salt transport occurs under electroneutral conditions and thus the effective diffusivity D is a combination of ionic diffusivities of the sodium (DNa+ ) and the chloride ions (DCl− ), and is given by the following expression

2.3. Water fraction measurements To determine the weight fraction of water (Q) in the hydrated gel, a dry gel of mass Wd was soaked in DI water overnight or longer to ensure equilibrium. The hydrated lens was then weighted and the equilibrium water fraction in the lens was calculated as Weq − Wd × 100 Weq

2.4.2. Ion transport in diffusion cell (direct permeation) The gel was soaked in DI water or in NaCl solutions of various concentrations overnight at room temperature. The fully hydrated gel was subsequently mounted in a horizontal diffusion cell, and then 18 ml of NaCl solution and 30 ml of DI water were placed into the donor and the receiver compartments, respectively, maintained at room temperature and stirred at 300 rpm. The NaCl concentration in the receiving compartment was determined as a function of time for 300 min by measuring the conductivity of the solution. 3. Results and discussion

or other desired size and shape by scissors for subsequent experiments. Prior to conducting further tests, the prepared hydrogel was soaked in ethanol for 3 h and then dried at ambient temperature overnight to remove the unreacted monomer.

Q [%] =

97

(1)

D=

2DNa+ DCl− DNa+ + DCl−

(2)

3.1. Comparison of transport measurements from the kinetic and permeation approaches for Gels A1–4 3.1.1. Kinetic approach for measuring salt diffusivity through release in perfect sink In this approach the lens was soaked in a salt solution till equilibrium, and the salt loaded lens was then soaked in DI water. Due to the large fluid volume during release, the entire salt loaded during soaking in salt solution was assumed to be released during the subsequent soaking in DI water. The salt partition coefficient K in silicone hydrogel can be determined by Vw Cr Vg Cl

where Weq is the mass of hydrated gel at equilibrium.

K=

2.4. Ion permeability measurements

where Vw and Vg are the volumes of the release medium and the fully hydrated gel, respectively, and Cr and Cl are the equilibrium concentrations of NaCl in the fluid in the release and loading steps, respectively. The above equation provides the partition coefficient in the gel at concentrations corresponding to the equilibrium concentration in loading. The dynamic salt transport can be considered as onedimensional transport since the diameter of the hydrogel sample is much larger than its thickness. Due to the complexity of the composition and microstructure of the silicone hydrogels, it is instructive to consider possible issues that could impact the rate limiting transport mechanisms. The ion transport leads to changes in the salt concentration in the gels, which alters the water content, leading to swelling or deswelling. The velocity driven by the swelling is typically not included in the model, and so it is instructive to explore the impact of the salt concentration, which controls the degree of swelling, on transport. Additionally, the ion transport could potentially include ion diffusion along with binding to the polymer chains, which could lead to electrostatic effects on transport. The binding kinetics could lead to concentration dependent partition coefficient, and thus a non-linear effect of concentration on transport. These issues could be explored by measuring transport at various salt concentrations and also for various gel thicknesses.

2.4.1. Salt release in perfect sink (kinetic desorption) The circular hydrogel of 1.65 cm diameter was soaked in 0.5 M, 0.75 M or 1.0 M NaCl solution until equilibrium was achieved. The salt-loaded gel was then transferred into a well mixed DI water sink maintained at room temperature and stirred at 300 rpm. The NaCl concentration of the aqueous medium was determined periodically by measuring the conductivity by Con 110 series sensor (OAKTON® ) and then related to concentration through the calibration curve, which was linear with a slope of 8.58 × 10−6 M/␮s. The ratio of the fluid to gel volume was chosen to be 80 and 600, for the loading and release phases, respectively. The thickness and diameter of the hydrated gel were measured before and after the experiment by a digimatic micrometer (Mitutoyo Corp., Kawasaki, Japan), and then the volume of hydrated gel was calculated by assuming the sample to be a disk. The thickness of the hydrated gel actually varies with the salt concentration, and thus the thickness changes with time during the experiment. However, within the range of salt concentrations explored here, the difference of the measured thickness caused by swelling is less than 5%. Thus, the model is based on a constant gel thickness and the average of the measured thickness before and after the experiment was used as the thickness.

(3)

98

C.-C. Peng, A. Chauhan / Journal of Membrane Science 399–400 (2012) 95–105 Table 2 Measured parameters for the Series A silicone hydrogels. Sample

Equilibrium water content, Q (%)

Partition coefficient, K

Diffusivity, D (×10−6 mm2 /min)

˛ (min)

A1 A2 A3 A4

22.5 19.7 16.6 11.1

0.1024 0.0834 0.0571 0.0338

1957.7 1012.1 621.9 36.1

0.160 0.007 0.283 0.018

Model: Based on the above results, the salt transport can be described by the diffusion equation, i.e., ∂C ∂2 C =D 2 ∂t ∂y

(4)

The boundary conditions for the release experiment are ∂C (t, y = 0) = 0 ∂y

C(t, y = h) = KCw

(5)

where h is the half-thickness of the gel. The first boundary condition assumes symmetry at the center of the gel and the second describes equilibrium of salt concentration between the gel and the aqueous phase. A mass balance on the aqueous reservoir in the beaker yields



Vw

dCw ∂C  = −2DAgel = dt ∂y 

(6) y=h

where Vw is the water volume in the beaker, Agel is the crosssectional area of the gel, and C and Cw are the sodium chloride concentration in the gel and aqueous phase, respectively. In addition, the initial conditions for the drug release experiments are C(y, t = 0) = Ci Fig. 1. Salt release profile from 0.13 mm-thick Gel A3 loaded with salt by soaking in solutions of various concentrations. The solid lines are the model prediction and all experiment data are presented as mean ± S.D. with n ≥ 3.

Effect of salt concentration: The effect of ionic strength on the ion transport of silicone hydrogel was studied by conducting salt release in perfect sink with A3 gels that were soaked in salt solutions of various concentrations. The release profiles of these gels are shown in Fig. 1. The normalized release profiles (C/Cf ), i.e., the ratio of the dynamic salt concentration in the bulk aqueous medium and the final equilibrium concentration in the bulk, overlap for various values of salt concentration (Fig. 1). This proves that within the concentration range explored here, the salt transport is linear in concentration suggesting that the binding kinetics of ions, electrostatic effects, and the potential deswelling of the gels due to salt loss does not appear to influence transport. It is noted that the diffusion coefficient of water in the gels is likely smaller than that of the salt and thus the gel hydration may not change during the experiment even though the salt concentration is changing. Effect of gel thickness: If the salt transport is diffusion controlled with constant diffusivity, the release time is proportional to the square of the gel thickness. To determine the rate limiting step, salt release profiles were measured from gels of different thickness while keeping the ratio of the fluid and the gel volume fixed for all thicknesses. The measured release profiles from A3 gels are plotted vs. scaled time, which is defined as time/(gel thickness/0.1 mm)2 , in Fig. 2. It is obvious that within the margins of experimental error, the scaled release profiles of the silicone hydrogels with different thickness overlap, proving that the dominating mechanism of ion transport of silicone hydrogel in perfect sink is the ion diffusion through the gel phase. Additionally, this also proves that mass transfer resistance in the fluid is negligible.

Cw (t = 0) = 0

(7)

Since the aqueous volume in the beaker is much larger than the gel volume, it is reasonable to assume that the concentration Cw is negligible in this perfect sink condition. The above set of equations can thus be solved analytically to yield C=

∞  (−1)n 4C

i

n=0

(2n + 1)

cos

 (2n + 1)  2h

2 2  )/4h2 )Dt

y e−(((2n+1)

2 2 8 (Ci Vgel )  1 2 (1 − e−(((2n+1)  )/4h )Dt ) Vf 2 (2n + 1)2

∞

Cw =

(8)

n=0

The unknown parameter D can be determined by fitting the measured Cw to the above equation. The fitting was done by mini mizing the error defined as



2

(1 − (Cw,ex /Cw ) )/N, where N is

the number of data points, and Cw,ex and Cw are the measured and predicted concentrations of NaCl, respectively. In addition, a parameter ˛ was introduced in the model to compensate for the possibility of experimental errors associated with an offset between the time t = 0 in the model and the time at which the experiment began. To include the offset, the time t in the fitting is equal to tapp − ˛, where tapp is the apparent experimental time. The above model was used to fit the experiment data to determine the D and ˛ of the silicone gel by using the function “fminsearch” in MATLAB® . The fitted release curves are compared with experimental data in Figs. 1 and 2, and the best-fit value of D for gel A3 was determined to be 611.1 ± 69.2 × 10−6 mm2 /min. The time offset for the fittings was 0.470 ± 0.169 min. The release profiles for other gels of the A series (Fig. 3) were also fitted to the diffusion model and the values of the fitted diffusivities and the time lag are summarized in Table 2, along with the values of the water content and the salt partition coefficient. The fitted release profiles are in good agreement with experimental data for all gels. The values of ˛, i.e., the

C.-C. Peng, A. Chauhan / Journal of Membrane Science 399–400 (2012) 95–105

99

Fig. 2. Salt release profiles from Gel A3 of different thickness. The gels were loaded with salt by soaking in 0.75 M salt solution. The solid lines are the model prediction and all experiment data are presented as mean ± S.D. with n ≥ 3.

which was then utilized to determine the dynamic receiver concentration (Cw ). The salt permeability (also referred to as the ionoflux diffusion coefficient, Dion ) was first determined by solving the diffusion equation under the pseudo-steady state conditions to give Dion =

Fig. 3. Salt release profiles under perfect sink from Gels A1–4. All samples were 0.13 mm thick and pre-soaked in 0.75 M NaCl(aq) . The solid lines are the model prediction and all experiment data are presented as mean ± S.D. with n ≥ 3.

time offset is less than 20 s, and it can likely be attributed to errors between the start of the clock and insertion of the sample in the release medium. 3.1.2. Permeation approach in a diffusion cell In this approach, the gels were mounted in a diffusion cell that contained salt solution in the donor compartment. The dynamic conductivity was measured in the receiver compartment (Fig. 4),

n A × dc/dx

where n is the rate of ion transport (= Vw dCw /dt), Vw and Cw are the volume and concentration in the receiver, A is the membrane area, dc/dx is the concentration gradient in the gel, and Dion is the permeability. The concentration gradient was assumed to equal the ratio of the initial donor concentration and the gel thickness based on the infinite sink assumption for both compartments. The linear fit for the measured conductivity (Fig. 4) was used to determine the values of Dion . The fitted values of permeability for Gels A1–4 obtained from the pseudo-steady state regime are 193.5, 112.3, 39.6 and 1.5 × 10−6 mm2 /min, respectively, and these values match the results of KD from the kinetic approach. The effect of salt concentration on salt transport during perfusion in a diffusion chamber was explored for Gels A3 (Fig. 5). The normalized concentration in the receiver, defined as ratio of the receiver and the initial donor NaCl concentrations, is plotted as a function of time. The results from various donor concentrations overlap within the margins of experiment error, suggesting that the ion transport of silicone hydrogel in diffusion cell is linear in the explored concentration range, in agreement with the findings from the kinetic release experiments. The pseudo-steady state transport across the gel depends only on the gel permeability, and thus the diffusion cell approach is typically utilized only for measuring the permeability KD. The initial transients in the receiver concentration before the pseudo-steady state is achieved however depend separately on K and D, and thus it might be feasible to utilize the entire transient data, including the short time data, to fit both K and D. If feasible, this may allow fully characterization of the transport by means of the diffusion cell experiments. The transport across the gel can be modeled by the diffusion equation (Eq. (4)), with the following boundary conditions: C(t, y = 0) = KCw

Fig. 4. Transient conductivity in the receiver compartment of the diffusion cell for Gels A1–4. All samples were 0.13 mm thick with no preloaded salt. The solid lines are the linear regression of data at pseudo-steady state. The NaCl concentration in the donor compartment was 0.5 M. All experiment data are presented as mean ± S.D. with n ≥ 3.

(9)

C(t, y = h) = KC ∗

(10)

where h is now the full thickness of the gel, C* is NaCl concentration in the donor compartment, and K is the salt partition coefficient of the gel. Both boundary conditions assume that the fluids in the reservoirs are in equilibrium with the contacting gel surface, and additionally the latter boundary condition assumes that the volume of the donor compartment is sufficiently large to be modeled as perfect source. A mass balance on the receiving compartment yields



Vw =

dCw ∂C  = −DA dt ∂y 

(11) y=0

100

C.-C. Peng, A. Chauhan / Journal of Membrane Science 399–400 (2012) 95–105

Fig. 5. Transient conductivity in the receiver compartment of the diffusion cell for Gels A3 with varying salt concentrations in the donor compartment. All samples were 0.13 mm thick with no preloaded salt. All experiment data are presented as mean ± S.D. with n ≥ 3.

where Vw is the DI water volume of the receiving compartment, A is the cross-sectional area of the gel, and Cw is the NaCl concentration in the receiving medium. Finally the initial conditions for the drug release experiments are C(y, t = 0) = KCi

Cw (t = 0) = 0

(12)

where Ci is the concentration of NaCl solution in which the gel was soaked overnight prior to conducting the diffusion cell experiment, and thus KCi is the initial salt concentration in the gel. The above set of equations can be considerably simplified by noting the salt concentration in the receiver compartment is much smaller than that in the donor, and thus the salt concentration in the gel at the interface contacting the receiver can be assumed to be zero. With thus simplification, the above equation set can be solved analytically to yield C=

∞  2K

n n=1

AK Cw (t) = Vw

[C ∗ cos(n) − Ci (cos(n) − 1)] sin



∞  n+1 (−1) 2h

(n)

2

∗

 n h

2

y e−(n/h)

[C cos(n) − Ci (cos(n)−1)] (e

Dt

+

C∗K y h

−(n/h)2 Dt



DC ∗ t −1)+ h

n=1

(13) At long times, when the pseudo-steady state is attained, Eq. (13) correctly reduces to Eq. (9), where KD = Dion . If the diffusion model (Eq. (13)) for salt transport in a diffusion cell holds, a plot of the scaled receiver concentration (Cw /h) vs. scaled time t/(h/h0 )2 , where h0 is an arbitrarily chosen reference thickness, should overlap for the same hydrogels of all thicknesses. Several experiments were conducted with Gel A3 of varying thicknesses,

Fig. 6. Salt transport in a diffusion cell for Gels A3 of different thicknesses. The plots show the salt concentration in the receiving reservoir/gel thickness against scaled time, defined as time/(gel thikness/0.1 mm)2 . The salt concentrations in the donor cell are (a) 0.25 M, (b) 0.5 M, (c) 0.25 M. The gel was equilibrated with DI water for (a) and (b) and with 0.25 M salt solution in (c) prior to mounting in the diffusion cell. The data with error bars is presented as mean ± S.D. with n ≥ 3.

including some in which the gels were preloaded with salt. The results from these experiments are shown in Fig. 6 in which the scaled concentrations are plotted against scaled time, with the reference thickness h0 chosen to be 0.1 mm. The overlap in scaled plots again suggests that the salt transport through the hydrogels in diffusion cell is a diffusion controlled process limited by gel diffusivity with negligible resistance in the fluid. Subsequently, the measured data for Cw , i.e., salt concentration in the receiver for the experiments sets shown in Fig. 6 was fitted to Eq. (13) to determine the unknown parameters K and D. While fitting the data, the product of K and D was fixed to equal the value obtained by fitting the

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101

A3 obtained through this fitting method were 0.0587 ± 0.0197 and 671.0 ± 254.3 × 10−6 mm2 /min, respectively. These average values are in reasonable agreement with the K and D obtained from kinetic desorption. Thus, we can obtain K and D separately in the diffusion cell permeation method by incorporating the initial transport data into the model fitting. The standard deviations in K and D are however larger than those from kinetic desorption experiments due to the difficulty in accurately measuring the small concentrations at short times. It is noted that the reliability of this approach increases by increasing the gel thickness which provides more short time data before pseudo steady state is reached. Also, utilizing a gel preloaded with salt increases the accuracy of the method because the concentrations in the receiver compartment are much larger at short times compared to the case in which a gel without preloaded salt is used. 3.2. Effect of composition of silicone hydrogel on ion permeability

Fig. 7. Salt transport in a diffusion cell for Gels A3 of different thicknesses. The salt concentrations in the donor cell are (a) 0.25 M, (b) 0.5 M, (c) 0.25 M. The gel was equilibrated with DI water for (a) and (b) and with 0.25 M salt solution in (c) prior to mounting in the diffusion cell. The solid lines are model fitting based on Eq. (13). The data with error bar represents mean ± S.D. with n ≥ 3.

pseudo-steady data. Thus the fitting of the short time data was done with only two fitting parameters; D and ˛ (time offset). The fitting was performed by using the function “fminsearch” in MATLAB® with the same error definition described earlier for the kinetic desorption model. The best fit results plotted in Fig. 7 agree reasonably well with the experimental data. The calculated time offset for these fittings is 2.10 ± 1.15 min, which is larger than that for the kinetic approach, but it can be attributed to the time required for assembling the lab-made diffusion cell. The average K and D for Gel

The results above show that both kinetic release and permeation approaches can be utilized to determine the salt diffusivity and partition coefficient in the gels. Below we use the kinetic approach to explore the effect of composition on salt transport in the siliconehydrogels. The experiments described below were conducted with 0.13 mm thick films, loaded with salt by soaking in 0.75 M solutions. For each gel, the water content and the salt partition coefficient were first measured, and then the release experiments were fitted to obtain the diffusivity. Fig. 8 shows the variations in water content, salt partition coefficient, diffusivity and the permeability with changes in composition of the gels. For this set of gels, the fraction TRIS + macromer was kept constant, while the ratio of these two components was varied. Since the amount of hydrophilic monomers (DMA and NVP) is fixed in this series of gels, the water content and NaCl partition coefficient should have only a slight dependency on the TRIS/macromer ratio. For example, an increase in TRIS/(TRIS + macromer) ratio from 0.25 to 0.75 only results in a 30% reduction in water content and NaCl partition coefficient. The slight decrease can be attributed to the higher hydrophobility of silicone than the macromer, which also has a hydrophilic segment. However, the fitted D exhibited a more complicated dependency on the TRIS/(TRIS + macromer) ratio, as shown in Fig. 8b. For the gels with TRIS/(TRIS + macromer) ratio less than 0.5, D decreases gradually likely due to the reduction in the water content. The D values however change more drastically for TRIS/(TRIS + macromer) ratios greater than 0.5, suggesting possible structural transitions. Since macromer is required to form an interface between the silicone regions and the hydrophilic DMA regions, a decrease in the macromer ratio beyond a critical value could lead to a transition from a bicontinuous structure to a dispersed structure, with either silicone or hydrophilic continuous phases depending on the ratio of DMA to TRIS. For the case of gels in Fig. 8, it appears that the transition is to a continuous DMA phase, and the reduction in ion diffusivity is due to the barrier offered by the dispersed TRIS phases in the gel. The effect of the crosslinker, EGDMA, on ion transport properties of the synthesized silicone hydrogel was also studied. Fig. 9 shows that both water content and NaCl partition coefficient decrease as the amount of EGDMA increases. This is expected because increased crosslinking reduces the length of the segment between crosslinks thereby decreasing pore size and the mobility of the crosslinked polymer chain, and thus leading to lower water content and salt solubility. However, the diffusivity trends are again different from the partition coefficient trends with a maximum in diffusivity at about 2% of EGDMA in the monomer mixture, as shown in Fig. 9b. The non-monotonic effects of crosslinker on diffusivity are also likely related to the changes in the microstructure of the gels.

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Fig. 8. (a) NaCl partition coefficient (K), (b) diffusivity (D), (c) ion permeability (KD), and (d) water content (Q) for Series B silicone hydrogels, i.e., gels with different TRIS/macromer ratios.

Finally, the effect of hydrophilic DMA composition in the hydrogel on sat transport was explored by preparing gels with randomly chosen DMA, TRIS and macromer ratios (Gel D1–D6), while the amount of NVP, EGDMA and initiator were kept the same, and the results are shown in Fig. 10. The results show that both water content and salt partition coefficient linearly depend on the DMA content in the gel. The salt diffusivity D also increases with DMA fraction but the slight non-linear dependence suggests that the gel structure in addition to the water content impacts diffusivity. Since

both K and D increase, the permeability of the gels KD shows a strong dependency on the DMA amount. 3.2.1. Relationship between water content and salt partition coefficient The results shown above demonstrate that the compositions of the gels affect the water content and also the salt partition coefficient and diffusivity. It could be anticipated that the both K and D depend on the composition due to the changes in water content

Fig. 9. (a) NaCl partition coefficient (K), (b) diffusivity (D), (c) ion permeability (KD), and (d) water content (Q) for series C silicone hydrogels, i.e., gels with different EGDMA fraction.

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Fig. 10. (a) NaCl partition coefficient (K), (b) diffusivity (D), (c) ion permeability (KD), and (d) water content (Q) for Series A and D silicone hydrogels, i.e., gels with different DMA fraction.

with composition, and that both K and D are unique functions of the water content. For instance, if the salt only partition in the water phase inside the gel matrix, the salt partition coefficient could be expected to equal the water fraction inside the hydrogel. The measured values of water content and the salt partition coefficient for all gels are plotted in Fig. 11. The plot shows that even though the salt partition coefficient is strongly correlated to the water content of these silicone hydrogels, the salt partition coefficient for all gels is below the water content. It is noted that water fraction was measured in DI water and its value will increase in salt solutions, but the increase is minor [13,14], and cannot explain the significant differences between the water content and the salt partition coefficient. Similar results have been reported in other hydrogel systems as well [11,13,14,20,21,25], and this deviation is attributed to the negative interactions between the polymer chains and the salt ions and also due to various states of water in the gel including the bound water that potentially does not contribute to salt partitioning [11].

3.2.2. Relationship between water content and salt diffusivity Based on the free volume theory model of hydrated polymer membranes proposed by Yasuda et al., the diffusion constant D of salt through the hydrated membrane can be written as a function of water volume fraction H as,

where ˇ is a proportionality constant for the gel, and D0 is the diffusion constant of sodium chloride in pure water, which is 1.5 × 10−5 cm2 /s at 25 ◦ C [31]. Thus, a plot of log D vs. 1/H is expected to be linear. Assuming comparable densities for the polymer and water, the volume fraction of water H can be approximated as the water content Q. Fig. 12 plots the salt diffusivity D on logarithmic scale vs. the reciprocal of water fraction (1/Q) of the silicone hydrogels. The data shows that the diffusivity decreases with decreasing water content, but the relationship between log(D)

Fig. 11. Relationship between salt partition coefficient (K) and water fraction (Q) of silicone hydrogel. The dash line indicates K = Q, and the solid line is draw for visual guidance.

Fig. 12. Relationship between salt diffusivity (D) and the reciprocal of water fraction (1/Q) of silicone hydrogels. The solid line is the linear best fit for data with Q greater than 0.15.



D = D0 exp −ˇ

1

H



−1

(14)

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Fig. 13. Relationship between salt permeability (KD) and reciprocal water fraction (1/Q) of silicone hydrogels. The solid line is the best linear fit for data with Q greater than 0.15. Published data from selected literature [7,10] is also included in the plot.

and 1/Q is not linear, particularly for the lower water fraction gels. For the gels with water fraction larger than 15%, which is typical for commercial silicone hydrogel contact lenses [7,32], the behavior is closer to being linear, and so a linear regression analysis was applied to determine the best fit between the data and the free volume theory (Eq. (14)). The best fit solid line is also not in good agreement with the data for gels with water content larger than 15%. The silicone hydrogels are non-homogeneous systems with hydrophobic silicone phase and the hydrophilic DMA phase, and thus the microstructure of the gels also impact the transport, in addition to the free volume. The ion permeability is the product of salt partition coefficient K and salt diffusion coefficient D. The dependence of K on water content is much weaker than that of D, and thus the relationship between salt permeability and water fraction can be also be approximately described by the free volume theory model (Fig. 13). In addition to the data from the gels discussed here, data from other prior publications and that for commercial lenses is also included [7,10]. The linear fit for high water content gels is also included in the figure. The data deviates significantly particularly at low water fractions because the microstructure of the gels contain phaseseparated regions. Additionally, the interaction between polymer matrix and salt also becomes more significant. Both conditions violate the assumptions of the free volume theory, which requires the hydrogel to be homogeneous and the interaction between polymer and solute should be negligible. Similar deviations from free volume theory were observed by Guan et al. who reported measurements of both partition coefficients and diffusivity of sodium chloride in several commercial contact lenses [11]. 4. Conclusions The ion permeability of contact lenses is critically important because it directly relates to the on-eye movement. The salt transport across the contact lens under in vivo conditions depends only on the permeability, which is the product of the partition coefficient and the diffusivity. However, measurements of both K and D are important to understand the details of the transport, particularly the impact of the microstructure on the salt transport. The transport of salt in the silicone-hydrogels is linear in concentration and controlled by diffusivity through the gels. The transport can be modeled with diffusion equation with concentration independent diffusion and partition coefficient. Also, swelling dynamics in the gel, which can cause convection as well as position dependent diffusivity due to spatial variations in water content can be neglected.

The partition coefficient and diffusivity of salt can be measured by the kinetic release experiments. Also, the salt permeability can be easily measured through permeation experiments in a diffusion cell by utilizing the pseudo-steady data. The permeability values obtained from the two methods agree with each other. We have also shown that the short-time data before pseudo-steady state is reached can be utilized to separately determine both the partition coefficient and the diffusivity. The silicone hydrogels are typically two-phase gels in which the silicone rich phase coexists with the hydrophilic phase. Since ions do not partition or diffuse through the silicone phase, the relative fraction of this phase and its distribution impacts the salt permeability. Here we show that slight changes in composition can lead to large changes in the salt diffusivity, likely due to transitions in the microstructure. The microstructure can be controlled by the relative amounts of the hydrophilic and the silicone monomers, and also the macromer, which is necessary for solubilization of the hydrophilic and the silicone monomers. The free volume theory cannot adequately relate the salt diffusivity to the water content for the silicone hydrogels because of the confounding role of the microstructure. The results on salt transport reported here are important in understanding transport of solutes through silicone hydrogels, and are particularly relevant to application of silicone hydrogels as contact lens materials. Due to the relationship between transport and microstructure in the silicone hydrogel lenses, direct measurements and quantification of the microstructure through imaging techniques could be valuable in developing quantitative relationships. Furthermore, simultaneous transport measurements of both hydrophobic and hydrophilic solutes could be useful in further understanding the impact of microstructure on transport as each solute will diffuse through different regions in the gel. Such studies will also be relevant to the use of silicone hydrogels for contact lenses, which need to have high ion and oxygen permeabilities, and also possibly low diffusivity for ophthalmic drugs to facilitate extended ophthalmic drug delivery. Acknowledgements This research was partially supported by the 2009 Opportunity Funds from the University of Florida and a Research Grant from Ciba Vision. We also thank Lynn Winterton for valuable discussions and his insights on the microstructure and ion transport in silicone hydrogel contact lenses. References [1] B.A. Holden, G.W. Mertz, Critical oxygen levels to avoid corneal edema for daily and extended wear contact-lenses, Invest. Ophthalmol. Vis. Sci. 25 (1984) 1161–1167. [2] D.M. Harvitt, J.A. Bonanno, Re-evaluation of the oxygen diffusion model for predicting minimum contact lens Dk/t values needed to avoid corneal anoxia, Optom. Vis. Sci. 76 (1999) 712–719. [3] P.C. Nicolson, J. Vogt, Soft contact lens polymers: an evolution, Biomaterials 22 (2001) 3273–3283. [4] A. Domschke, D. Lohmann, L. Winterton, On-eye mobility of soft oxygen permeable contact lenses, in: Proceedings of the ACS Spring National Meeting, PMSE, San Francisco, 1997. [5] B. Tighe, Silicone hydrogel materials – how do they work? in: S. David (Ed.), Silicone Hydrogels: The Rebirth of Continuous Wear Contact Lenses, Betterworth Heinemann, Oxford, 2000, pp. 1–21. [6] P. Nicolson, R.C. Baron, P. Chabrecek, J. Court, A. Domscheke, H.J. Criesser, Extended wear ophthalmic lens, US Patent No. 5,760,100 (1998). [7] C.C. Peng, J. Kim, A. Chauhan, Extended delivery of hydrophilic drugs from silicone-hydrogel contact lenses containing Vitamin E diffusion barriers Biomaterials 31 (2010) 4032–4047. [8] S.L. Willis, A novel phosphorylcholine-coated contact lens for extended wear use, Biomaterials 22 (2001) 3261–3272. [9] M. Ali, S. Horikawa, S. Venkatesh, J. Saha, J.W. Hong, M.E. Byrne, Zero-order therapeutic release from imprinted hydrogel contact lenses within in vitro physiological ocular tear flow, J. Control. Release 124 (2007) 154–162.

C.-C. Peng, A. Chauhan / Journal of Membrane Science 399–400 (2012) 95–105 [10] J. Kim, A. Conway, A. Chauhan, Extended delivery of ophthalmic drugs by silicone hydrogel contact lenses, Biomaterials 29 (2008) 2259–2269. [11] L. Guan, M.E. Jiménez, C. Walowski, A. Boushehri, J.M. Prausnitz, C.J. Radke, Permeability and partition coefficient of aqueous sodium chloride in soft contact lenses, J. Appl. Polym. Sci. 122 (2011), doi:10.1002/app.33336. [12] T. Tanaka, Encyclopedia of Polymer Science and Engineering, vol. 6, Wiley, New York, 1986, p. 514. [13] H. Ju, A.C. Sagle, B.D. Freeman, J.I. Mardel, A.J. Hill, Characterization of sodium chloride and water transport in crosslinked poly(ethylene oxide) hydrogels, J. Membr. Sci. 358 (2010) 131–141. [14] A.C. Sagle, H. Ju, B.D. Freeman, M.M. Sharma, PEG-based hydrogel membrane coatings, Polymer 50 (2009) 756–766. [15] R.J. Petersen, Composite reverse osmosis and nanofiltration membranes, J. Membr. Sci. 83 (1993) 81–150. [16] W.R. Clark, R.J. Hamburger, M.J. Lysaght, Effect of membrane composition and structure on solute removal and biocompatibility in hemodialysis, Kidney Int. 56 (1999) 2005–2015. [17] S.M. Murphy, C.J. Hamilton, M.L. Davies, B.J. Tighe, Polymer membranes in clinical sensor applications. II. The design and fabrication of permselective hydrogels for electrochemical devices, Biomaterials 13 (1992) 979–990. [18] P. Lopour, V. Janatova, Silicone rubber-hydrogel composites as polymeric biomaterials. VI. Transport properties in the water-swollen state, Biomaterials 16 (1995) 633–640. [19] P. Lopour, P. Vondracek, V. Janatova, J. Sulc, J. Vacik, Silicone rubber-hydrogel composites as polymeric biomaterials. II. Hydrophilicity and permeability to water-soluble low-molecular-weight compounds, Biomaterials 11 (1990) 397–402. [20] H. Yasuda, L.D. Ikenberry, C.E. Lamaze, Permeability of solutes through hydrated polymer membranes. Part II. Permeability of water soluble organic solutes, Die Makromol. Chem. 125 (1969) 108–118.

105

[21] H. Yasuda, C.E. Lamaze, L.D. Ikenberry, Permeability of solutes through hydrated polymer membranes. Part I. Diffusion of sodium chloride, Die Makromol. Chem. 118 (1968) 19–35. [22] H.K. Lonsdale, U. Merten, R.L. Riley, Transport properties of cellulose acetate osmotic membranes, J. Appl. Polym. Sci. 9 (1965) 1341–1362. [23] M.L. Cheng, Y.M. Sun, Observation of the solute transport in the permeation through hydrogel membranes by using FTIR-microscopy, J. Membr. Sci. 253 (2005) 191–198. [24] Y.M. Sun, J.N. Chang, Solute transport in poly(2-hydroxyethyl methacrylate) hydrogel membranes, J. Polym. Res. 2 (1995) 71–82. [25] K. Nagai, S. Tanaka, Y. Hirata, T. Nakagawa, M.E. Arnold, B.D. Freeman, D. Leroux, D.E. Betts, J.M. DeSimone, F.A. DiGiano, Solubility and diffusivity of sodium chloride in phase-separated block copolymers of poly (2-dimethylaminoethyl methacrylate), poly(1,1 -dihydroperfluorooctyl methacrylate) and poly(1,1,2,2-tetrahydroperfluorooctyl acrylate), Polymer 42 (2001) 09941–09948. [26] R.W. Baker, Membrane Technology and Applications, Wiley, 2004. [27] B. Amsden, Solute diffusion within hydrogels. Mechanisms and models, Macromolecules 31 (1998) 8382–8395. [28] M.H. Cohen, D. Turnbull, Molecular transport in liquids and glasses, J. Chem. Phys. 31 (1959) 1164–1169. [29] J. Kim, A. Chauhan, Dexamethasone transport and ocular delivery from poly(hydroxyethyl methacrylate) gels, Int. J. Pharm. 353 (2008) 205–222. [30] C.C. Li, A. Chauhan, Modeling ophthalmic drug delivery by soaked contact lenses, Ind. Eng. Chem. Res. 45 (2006) 3718–3734. [31] C.J.D. Fell, H.P. Hutchison, Diffusion coefficients for sodium and potassium chlorides in water at elevated temperatures, J. Chem. Eng. Data 16 (1971) 427–429. [32] L. Jones, K. Dumbleton, M.M. Hom, A. Bruce, Soft lens extended wear and complications, in: Manual of Contact Lens Prescribing and Fitting, ButterworthHeinemann, Boston, 2006, pp. 393–441.