Multi-Effect-Coupling pH-Stimulus (MECpH) Model for pH-Sensitive Hydrogel
2.5 Parameter Studies by Steady-State Simulation for Equilibrium of Hydrogelfor Equilibrium of Hydrogel
2.5.3 Influence of Initial Geometry of Hydrogel
0 2 4 6 8 10 12 400
500 600 700 800 900 1000 1100 1200
Hdrogel diameter (μm)
pH Normalized Young modulus:
E/E0=0.7 E/E0=1.5 E/E0=3.0 E/E0=6.0
(a)
0 2 4 6 8 10 12 14 16 18 20
500 600 700 800 900 1000 1100 1200
Hydrogel diameter (μm)
Normalized Young modulus, E/E0 pH3 pH7 pH12
(b)
Fig. 2.13 Dependence of swelling on (a) bathing pH as the function of normalized Young’s modulus(E/E0)and (b) varying normalized Young’s modulus(E/E0)in acidic, neutral and basic solutions
different buffer systems as illustrated in Fig. 2.14. Influence of buffer contents on the swelling equilibrium at higher pH is more significant than that at lower pH. When the pH of buffer solutions is low, the degree of swelling of the hydrogel is almost insignificant even in different buffer systems and Young’s moduli. If the pH is high, the obvious differences in the degree of swelling are observed for different buffer systems. Further, the Britton–Robinson is the unchanging leader for providing the better buffer solution when large swelling scale is required. It should be pointed out that the influence of the buffer contents vanishes if Young’s modulus is high enough.
0 2 4 6 8 10 12 14 16 18 20 500
502 504 506 508 510
Hydrogel diameter (μm)
Normalized Young modulus, E/E0 Ideal solution Phosphate buffer Britton-Robinson buffer
(a)
0 2 4 6 8 10 12 14 16 18 20
500 600 700 800 900 1000 1100 1200 1300 1400 1500
Hydrogel diameter (μm)
Normalized Young modulus, E/E0 Ideal solution Phosphate buffer Britton-Robinson buffer
(b)
Fig. 2.14 Influences of buffer systems on swelling equilibrium as the function of normalized Young’s modulus (E/E0)in (a) acidic medium of pH 3 and (b) basic medium of pH 9
immersed in solution. The bathing solution is the electrolyte which is composed of NaCl and/or HCl. For the three pH buffered conditions, pH 3, 7 and 12, the con- centrations of cations inside the hydrogel are higher, whereas those of anions are lower in comparison with those in the external solution. These are the performance expected because of the negative sign of the ionized charge groups dangling on the network matrix of the PHEMA hydrogel. Similarly, the electric potential exists as long as the migrations of ions occur between the interior hydrogel and the exterior solution.
Since both the hydration and fixed charge concentration kept almost constant against different initial geometries of the hydrogel as shown in Figs. 2.17 and 2.18, the swelling of the hydrogels behaves negligibly when they are soaked in electrolyte solution. The characteristics are found more clearly in Fig. 2.18, where the hydrations of the swollen hydrogels are plotted against the different pH levels
0.0 0.2 0.4 0.6 0.8 1.0 1.00
1.01 1.02 1.03 1.04 1.05 1.06
Hydrogen ion concentration (mM)
Normalized distance across the hydrogel
0.0 0.2 0.4 0.6 0.8 1.0
298 300 302 304 306 308 310 312 314 316
Sodium ion concentration (mM)
Normalized distance across the hydrogel
0.0 0.2 0.4 0.6 0.8 1.0
288 290 292 294 296 298 300 302
Chloride ion concentration (mM)
Normalized distance across the hydrogel
0.0 0.2 0.4 0.6 0.8 1.0
0 5 10 15 20 25 30
Normalized distance across the hydrogel
0.0 0.2 0.4 0.6 0.8 1.0
–1.2 –1.0 –0.8 –0.6 –0.4 –0.2 0.0
Normalized distance across the hydrogel
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.00
0.05 0.10 0.15 0.20 0.25
Normalized distance across the hydrogel
(c) Chloride ion (cCl–)
Fixed-charge concentration (mM)
(d) Fixed charge group (cf) (a) Hydrogen ion (cH+) (b) Sodium ion (cNa+)
Electric potential (mV)
(e) Electric potential (ψ)
Displacement (μm)
(f) Displacement (u)
Dry gel diameter;
200μM 400μM 600μM
Dry gel diameter;
200μM 400μM 600μM
Dry gel diameter;
200μM 400μM 600μM
Dry gel diameter;
200μM 400μM 600μM
Dry gel diameter;
200μM 400μM 600μM
Dry gel diameter;
200μM 400μM 600μM
Fig. 2.15 Distributive profiles of cH+,cNa+,cCl−,cf,ψand u as the function of initial diameter of the dry gel, where the PHEMA hydrogel is equilibrated in an acidic medium of pH 3 with NaCl added to control the ionic strength
and dry gel diameters. As mentioned before, the diameters of dry gel are deter- mined by the diameters of the nominal photomasks and the hydration is calculated by H=Vf/Vs.
In order to understand the responsive characteristics of the hydrogel bathed in different buffer solution systems, several simulations are carried out to predict the
0.0 0.2 0.4 0.6 0.8 1.0 0.10
0.12 0.14 0.16 0.18 0.20
Hydrogen ion concentration (mM)
Normalized distance across the hydrogel Dry gel diameter:
200 μm 400 μm 600 μm
×10–3
(a) Hydrogen ion (cH+)
0.0 0.2 0.4 0.6 0.8 1.0
300 350 400 450 500 550
Sodium ion concentration (mM)
Normalized distance across the hydrogel
(b) Sodium ion (cNa+)
0.0 0.2 0.4 0.6 0.8 1.0
160 180 200 220 240 260 280 300 320
Chloride ion concentration (mM)
Normalized distance across the hydrogel
(c) Chloride ion (cCl–)
0.0 0.2 0.4 0.6 0.8 1.0
–50 0 50 100 150 200 250 300 350 400
Fixed-charge concentration (mM)
Normalized distance across the hydrogel
(d) Fixed charge group (cf)
0.0 0.2 0.4 0.6 0.8 1.0
–16 –14 –12 –10 –8 –6 –4 –2 0 2
Electric potential (mV)
Normalized distance across the hydrogel
(e) Electric potential (ψ)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Displacement (mm)
Normalized distance across the hydrogel
(f) Displacement (u)
Dry gel diameter:
200 μm 400 μm 600 μm
Dry gel diameter:
200 μm 400 μm 600 μm
Dry gel diameter:
200 μm 400 μm 600 μm
Dry gel diameter:
200 μm 400 μm 600 μm
Dry gel diameter:
200 μm 400 μm 600 μm
Fig. 2.16 Distributive profiles of cH+,cNa+,cCl−,cf,ψand u as the function of initial diameter of the dry gel, where the PHEMA hydrogel is equilibrated in a neutral medium with NaCl added to control the ionic strength
dilation of the hydrogels soaking in the phosphate buffer and Britton–Robinson buffer solutions. Figure 2.19 provides the comparison of swelling degree of the hydrated hydrogel for the three buffer solutions at pH 3 and 9 levels. The fig- ure shows the significant independency of swelling on the initial diameters of the hydrogels. Similar to the previous discussions, the Britton–Robinson buffer always demonstrates a potentiality as buffer environment solution to meet the need of voluminous swelling.
1.0 1.2 1.4 1.6 1.8
Hydrogen ion concentration (mM)
Normalized distance across the hydrogel Dry gel diameter:
200 μm 400 μm 600 μm
×10–9
300 350 400 450 500 550
Sodium ion concentration (mM)
Normalized distance across the hydrogel
(a) Hydrogen ion (cH+) (b) Sodiumion (cNa+)
160 180 200 220 240 260 280 300 320
Chloride ion concentration (mM)
Normalized distance across the hydrogel
–50 0 50 100 150 200 250 300 350 400
Fixed-charge concentration (mM)
Normalized distance across the hydrogel
(c) Chloride ion (ccl–) (d) Fixed charge group (cf)
–16 –14 –12 –10 –8 –6 –4 –2 0 2
Electric potential (mV)
Normalized distance across the hydrogel
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Displacement(mm)
Normalized distance across the hydrogel
(e) Electric potential (ψ) (f) Displacement (u)
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Dry gel diameter:
200 μm 400 μm 600 μm
Dry gel diameter:
200 μm 400 μm 600 μm
Dry gel diameter:
200 μm 400 μm 600 μm
Dry gel diameter:
200 μm 400 μm 600 μm
Dry gel diameter:
200 μm 400 μm 600 μm
Fig. 2.17 Distributive profiles of cH+,cNa+,cCl−,cf,ψand u as the function of initial diameter of the dry gel, where the PHEMA hydrogel is equilibrated in a basic medium of pH 12 with NaCl added to control the ionic strength