Supplementry Mteril (ESI) for Soft Mtter This journl is The Royl Society of hemistry 009 Supplementry dt Quntifying Hydrogel Response using Lser Light Scttering. Joshu M. G. Swnn, Wim Brs b, Jonthn R. Howse c*, Pul D. Tophm d* nd Anthony J. Ryn Deprtment of hemistry, University Of Sheffield, Sheffield, S3 7HF, U, nd b DUBBLE RG, ESRF, 6 rue Jules Horowitz, BP 0, F38043 Grenoble édex 9, Frnce nd c Deprtment of hemicl nd Process Engineering, University of Sheffield, Sheffield, S1 3JD, U Emil: j.r.howse@shef.c.uk nd d hemicl Engineering nd Applied hemistry, Aston University, Birminghm, B4 7ET, U. Emil: p.d.tophm@ston.c.uk Generl procedure for preprtion of monobsic buffer solutions The generl method used to prepre monobsic buffers is detiled below, n exmple is included for the preprtion of 0.05 M ethnol mine buffer, t ph 10, using Nl to fix the overll ionic strength to 0.1 M (prepred t 5 o ). Step 1: The p of ethnol mine (9.50 1 ) ws thermodynmiclly djusted for temperture nd ionic strength using the DebyeHuckel reltionship shown in eqution 1, where p 1 is the modified p, z is the chrge on the conjugte cid, I is the ionic strength of the solution nd A is constnt which hs vlue of 0.5114 t 5 o. A I p 1 = p + ( z 1) 0. 1 Ι 1+ I (1) p = + 0 5114 1 0 1 9. 5 (( 0) 1).. 0. 1 1. 0 () 1+ 1. 0 p 1 = 9. 61 (3) Step : The HendersonHsselblch reltionship (eq. 4) ws then used to determine the concentrtion of bse [A ] nd cid [HA] in the buffer t the given ph nd the totl buffer concentrtion (i.e. ph 10 t totl buffer concentrtion of 0.05M).
Supplementry Mteril (ESI) for Soft Mtter This journl is The Royl Society of hemistry 009 [ ph] [ A ] p + log10 (4) [ HA] = Eqution 4 implies tht the cid component of the buffer is neutrl, nd the bsic component hs negtive chrge. While this is true for mny buffers, in the cse of ethnol mine for exmple, the bsic component is neutrl nd the cid component is chrged (+1). For clrity the HendersonHsselblch eqution my be rewritten s shown in eqution 5, where A, defined s proton cceptor from BronstedLowry theory represents the bse. [ [ bse] p + log (5) [ cid] ph] = 10 The totl concentrtion of cid nd bse in the buffer is given by eqution 6. = [ HA ] + [ A ] (6) buffer The concentrtion of cid [HA] is relted to the concentrtion of hydrogen ion [H + ] nd bse [A ] through the equilibrium constnt,, see eqution 7. + [ H ][ A ] [ HA] = (7) Rerrngement, followed by substitution of eqution 7 into 6 llows the concentrtion of bse to be determined. + [ H ][ A ] buffer = + [ A ] (8) [ ] [ A buf ] = + + [ H ] (9) [ A 10 [ 0. 05][. 45 10 ] ] = (10) 10 10 [. 45 10 ] + [ 1 10 ] [ A ] = 0.0354M (11) [ HA] + [ A ] = 0.05M (1) [ HA ] = 0.0146 M (13) Step 3: Using this informtion the ionic strength of the buffer species cn then be determined.
Supplementry Mteril (ESI) for Soft Mtter This journl is The Royl Society of hemistry 009 The ionic strength describes the overll ionic properties of the solution. It is function of the concentrtion of ll individul species dissolved in solution; encompssed in eqution 14. 1 n c i 1 i z = i I = ( ) (14) where c i is the concentrtion of the ionic species, i, nd z i is the chrge on tht ion. The totl ionic strength is tken s the sum of ll species. In this exmple the concentrtion of [bse] nd [cid] is 0.0354 M nd 0.0146 M, respectively. The finl buffer cn be prepred in wys (1) by dissolving the required mount of bsic nd cidic components in solution to give finl solution t the correct ph, () dissolve the required mount of bsic or cid component in solution, then titrte it to the required ph using either strong cid or bse. In the cse of citric cid buffer, the only ions which contribute to the ionic strength re protonted ethnol mine (HOH NH 3 + ) nd chloride nion (l ). There ionic strength is clculted below, 1 + I = ( HOH NH3 1 ) + (l 1 ) (15) 1 I = ( 0. 0146 1 ) + ( 0. 0146 1 ) (16) I = 0.015M (17) As, I totl = I buffer + I slt, (18) where I buffer nd I slt re the ionic strength due to the dded slt nd buffer species cting lone, respectively. This indictes tht nother 0.085 M of Nl must be dded to mintin n ionic strength of 0.1 M Generl procedure for preprtion of multivlent buffer solutions
Supplementry Mteril (ESI) for Soft Mtter This journl is The Royl Society of hemistry 009 The method used to prepre multivlent buffers is more complicted. A full derivtion will not be given here but the following equtions describe the generl principles. Equtions (193) describe how the frctionl composition of ech ionic species (H 3 A, H A nd A 3 ) in trivlent buffer, such s citric cid used in this study, vry with chnges in p, (thermodynmiclly corrected), the totl concentrtion of hydronium ion given by D, nd the totl buffer concentrtion []. 3 The frctionl composition of ech species multiplied by the totl buffer concentrtion [] gives the concentrtion of ech species in solution (mol dm 3 ). The concentrtion of ech individul species cn then be inserted into eqution 14, to give the ionic strength. Summtion of the ionic strength for ech species gives I buffer (eqution 18). From I buffer one cn determine the mount of slt tht must be dded to mintin fixed ionic strength. re must be tken to use the correct chrge nd include ll the counterions. 3 = D + D + D + 1 1 1 3 (19) [ H3A] f ( H 3A) = = 3 D (0) [ HA ] f ( H A ) = = D 1 (1) D [ HA ] f ( HA ) = = 1 () 3 3 [ A ] f ( A ) = = 1 3 (3)
Supplementry Mteril (ESI) for Soft Mtter This journl is The Royl Society of hemistry 009 Buffer recipe used to mesure the effect of slt identity on the sttic response of the diffrction grting Tble 1. Amount of citric cid nd dded slt required to mintin fixed buffering cpcity nd ionic strength in 100 ml solution. Slt NAce Nl NNO 3 NBr NI NSN ph 3.6 3.6 3.6 3.6 3.6 3.6 oncentrtion of buffer required/ M 0.01 0.01 0.01 0.01 0.01 0.01 Ionic strength of buffer due to buffer species lone/ M 0.01 0.01 0.01 0.01 0.01 0.01 Required Ionic Strength/ M Amount of citric cid/ g Amount of dded slt/ g 0.1 0.1 0.1 0.1 0.1 0.1 1.9 1.9 1.9 1.9 1.9 1.9 0.74 0.5 0.76 0.9 1.34 0.73 Buffer recipe used to mesure the dynmic response of the diffrction grting Tble. Amount of buffer nd Nl required to mintin fixed buffering cpcity nd ionic strength in 100 ml solution. Buffer Ethnol mine itric cid ph 11. 3.6 oncentrtion of buffer required/ M 0.05 0.05 Ionic strength of buffer due to buffer species lone/ M 0.0013 0.05 Required Ionic Strength/ M 0.1 0.1 Amount of buffer/ g 0.31 0.96 Amount of Nl/ g 0.60 0.8 References
Supplementry Mteril (ESI) for Soft Mtter This journl is The Royl Society of hemistry 009 1. J. A. Den, Lnge s Hndbook of hemistry, McGrwHill, New York, 1973.. R. J. Beynon nd J. S. Esterby, Buffer Solutions, IRL Press, New York, 1996. 3. P Atkins nd J d. Pul, Elements of Physicl hemistry, 3 ed, Oxford University Press, Oxford, 000.