Colloidal Interactions in Solutions

Transcription

1 Colloidal Inteactions in Solutions Yun Liu National Institute of Standads and Technology (NIST) Cente fo Neuton Reseach Depatment of Mateials Science and Engineeing Univesity of Mayland, College Pak Tutoial Session, ACNS, 28, Santa Fe

2 Outline. Intoduction 2. Contast tem 3. Fom facto P(Q) 4. Stuctue facto S(Q) 5. Colloidal inteactions 6. Calculate stuctue facto S(Q) 7. Examples 8. Relations with some othe methods 9. Summay

3 . Intoduction: Small Angle Neuton Scatteing Spectomete NCNR NIST ( 2D image D data I(Q x,q y ): intensity distibution Annulus aveage (cm - ) k f θ Q Q (Å - ) k i

4 . Intoduction: What SANS measues? (Scatteed neuton intensity distibution) ( - ) = A P(Q) S(Q)

5 . Intoduction: Factoization Appoximation = A P(Q) S(Q) A: contast tem A = nv 2 2 Δρ n: numbe density v: volume of a colloidal paticle Δρ: scatteing length density diffeence P(Q): Nomalized fom facto (o inta-paticle stuctue facto) 2 3 iq P( Q) = ρ( ) e d / ρ( ) d 3 2 ρ P(Q) -2-4 R=4Å R S.-H. Chen Ann. Rev. Phy. Chem Q (Å - )

6 . Intoduction: Factoization Appoximation = A P(Q) S(Q) S(Q): Inte-paticle stuctue facto detemined by inte-paticle potential. S( Q) = N = + j, k N = + n e iq j k e j e iq iq e ( g( ) ) e j k iq k iq d 3 n: numbe density g(): pai distibution function S.-H. Chen Ann. Rev. Phy. Chem

7 2. Contast: Selectively obseve a stuctue = A P(Q) S(Q). A: Contast tem 2 2 A = nv Δρ Change scatteing length density: isotope eplacement

8 2. Contast: Selectively obseve a stuctue = A P(Q) S(Q) By changing elative atio of D 2 O/H 2 O, the scatteing length density can vay in a lage ange to match the scatteing length density of diffeent mateials. View gaph fom Chales Glinka

9 3. Fom facto: shape, volume, density pofile = A P(Q) S(Q) P(Q): Nomalized fom facto (o inta-paticle stuctue facto) At dilute concentation, S(Q). Theefoe, =A P(Q). Shape, volume, density pofile (Not necessaily spheical paticles). J. S. Pedeson, Adv. Colloid Inteface Sci. 7, 7-2 (997). (Fom factos of 26 models ae pesented in this pape).

10 3. Fom facto: Guinie plot Radius of gyation R G : a measue of size of an object 2 2 R G = γ ( ) i i (Weighted by the neuton scatteing length) i When Ql <<, whee l is the lagest length scale in a measued object, I( Q) = Aexp( RGQ ) o ln( I( Q) = ln( A) RGQ 3 3 P(Q) -2 R=4Å ln() -2-4 Slope: 3 2 R G Q (Å - ) Guinie plot x -3 Q 2 (Å -2 )

11 3. Fom facto: Guinie plot (cont d) ) QL << (Guinie egion) I( Q) = Aexp( 3 R 2 Q 2 G ) 2) QL >> & Qd << I( Q) π exp( QL 3) Qd >> 2 8cos ( Qd) I( Q) 4 3 Q Ld 6 Q 2 d 2 ) (Pood law: Q -4 decay) View gaph fom Chales Glinka

12 4. Stuctue facto S(Q): inte-paticle potential = A P(Q) S(Q). A: Contast tems 2. P(Q): Fom facto (o inta-paticle stuctue facto) 3. S(Q): Inte-paticle stuctue facto S( Q) = N = + j, k N = + n e iq j k e j e iq iq e ( g( ) ) e j k iq k iq d n: numbe density g(): pai distibution function 3

13 5. Colloidal inteactions: effective potential Z p Z p σ Coloumb inteaction: Sceened Coloumb inteaction: (Yukawa potential fom) Z pz p U ( ) = >, epulsive 4πε U ( ) = K e κ ( σ ) >, epulsive The Coloumb inteaction is sceened by counteions and coions in solutions and decays much faste than the bae inteaction.

14 5. Colloidal inteactions: Why study effective potential

15 5. Colloidal inteactions: Why study effective potential Single Paticle Infomation: Chage, Suface Popeties,

16 5. Colloidal inteactions: Why study effective potential Single Paticle Infomation: Chage, Suface Popeties, Collective Behavios: Diffusion, Clusteization,

17 5. Colloidal inteactions: Why study effective potential Single Paticle Infomation: Chage, Suface Popeties, Collective Behavios: Diffusion, Clusteization, Phase Behavios: Liquid, Cystal, Glass,

18 5. Colloidal inteactions: typical colloidal inteaction potential. Had Sphee Potential (Excluded volume effect) + V ( ) = < σ > σ Most colloids ae igid objects: poteins, silicon nano-paticle,

19 5. Colloidal inteactions: typical colloidal inteaction potential 2. Soft Coe Potential V ( ) = f ( ) < σ > σ Sta polymes, dendimes C. N. Likos, Soft Matte 2, 478 (26)

20 > < < < = a a a a V σ σ σ τ β 2 ln ) ( 2. Sticky Had Sphee, Shot-Range Attaction 5. Colloidal inteactions: typical colloidal inteaction potential Van de Waals attaction, depletion foce (entopic foce) Van de Waals attaction: momentay attaction due to unevenly distibuted electons in an atom o molecule. Exists between any two atoms o molecules unde any cicumstances.

21 5. Colloidal inteactions: typical colloidal inteaction potential 2. Sticky Had Sphee, Shot-Range Attaction Depletion foce: the ovelap of the depletion zones between lage paticles Inceases the system entopy and thus geneates the effective attaction. Lage paticle:. μm diamete Small paticle:.83 μm diamete J. C. Cocke et al., Phys. Rev. Lett. 82, 4352 (999)

22 5. Colloidal inteactions: typical colloidal inteaction potential 3. Electostatic inteaction Sceened Coloumb inteaction: U ( ) = K e κ ( σ ) The Coloumb inteaction is sceened by counteions and coions in solutions and decays much faste than the bae inteaction. (Yukawa potential fom) Poteins, chaged micelles, silica paticles, Reliably to extact EFFECTIVE CHARGE of a paticle! Lysozyme potein

23 5. Colloidal inteactions: DLVO potential (Inteaction between chaged colloidal paticles) Dejaguin-Landau-Vewey-Ovebeek potential (E. J. W. Vewey and J. TH. G. Ovebeek, Theoy of the Stability of Lyophobic Colloids, Elsevie, Amstedam, 948). Van de Waals foce (attactive) 2. Sceened Coloumb inteaction (epulsive) U A A = [ DLVO potential: + 2ln( )] 2 U = U + U DLVO A R U R = K e κ ( σ ) whee K = Z 2 λ B exp( κσ ) 2 ( + κσ ) Stong epulsion Weak epulsion

24 5. Colloidal inteactions: A geneal featue Had/Soft coe potential: Dendime, Sta polymes Electostatic epulsion Shot-ange attaction: Van de-waals attaction Depletion foce, Like chaged paticles Inteaction Range

25 6. Calculate the stuctue facto S(Q): Onstein-Zenike equation 3 3 ) ( ) ) ( ( ) ( d e h n d e g n Q S iq iq + = + = + = 3 ' ') ( ) ' ( ) ( ) ( d h c n c h Onstein-Zenike equation: Closues: link pai inteaction potential with h() and c(). MSA closue (Mean Spheical Appoximation) RY closue (Roges-Young) HNC closue (Hypenetted-Chain) )) ( ln( ) ( ) ( ) ( h h T k u c B + + = T k u c B ) ( ) ( = PY closue (Pecus-Yevic) ) ) ( )( ( ) ( ) ( + = h e c T k u B Othe closues: Zeah-Hansen, SMSA, SCOZA, HMSA, Refeence: C. Caccamo, Integal Equation Theoy Desciption of Phase Equilibia in Classical Fluids, Physics Repot 274, -5 (996). J. P. Hansen, I. R. McDonald, Theoy of Simple Liquids (Academic Pess, London) 976

26 6. Calculate the stuctue facto S(Q): Some Analytical Solutions to OZ Equation. Had sphee system: J. K. Pecus, G. J. Yevick, Phys. Rev., (958) J. P. Hansen, I. R. McDonald, Theoy of Simple Liquids (Academic Pess, London) 976 (PY Closue) 2. Sticky had sphee system: R. J. Baxte, J. Chem. Phys. 49, 277 (968) (PY Closue) 3. Shot-ange attaction system: Y. C. Liu, S. H. Chen, J. S. Huang, Phys. Rev. E 54, 698 (996) (PY Closue) 4. Had-coe Yukawa Inteaction: One Yukawa: E. Waisman, Mol. Phys. 25, 45 (973). Two Yukawa: J. S. Høye, G. Stell, and E. Waisman, Mol. Phys. 32, 29 (976) Multiple Yukawa: J. S. Høye and L. Blum, J. Stat. Phys. 6, 399 (977) (MSA Closue) Implementing the algoithms is sometimes non-tivial.

27 6. Calculate the stuctue facto S(Q): One Yukawa Had-Coe Potential: Hayte-Penfold Method J. B. Hayte and J. Penfold, Mol. Phys. 46, 65 (98). ( Cuent citation numbe: > 6) One Yukawa Had-Coe Potential It is a poweful method fo chaged colloidal system. Combing with othe theoies, the effective chage of a colloidal paticle could be obtained.. The DLVO theoy: κ ( σ ) e 2 exp( κσ ) U R = K whee K = Z λb 2 ( + κσ ) It woks at the dilute concentations. 2. The Genealized One Component Macoion (GOCM) theoy (O Rescaling Mean Spheical Appoximation (RMSA) theoy) Belloni, L. J. Chem. Phys. 986, 85, Chen, S.-H.; Sheu, E. Y. In Micella Solutions and Micoemulsions- Stuctue, Dynamics, and Statistical Themodynamics; Chen, S.-H., Rajagopalan, R., Eds.: Spinge-Velag: New Yok, 99

28 6. Calculate the stuctue facto S(Q): Two Yukawa Had-Coe Potential Y. Liu, W. R. Chen, S. H. Chen, J. Chem. Phys. 22, 4457 (25) It is useful fo system with complicated potential.. Chage colloidal paticles with a shot-ange attaction. 2. Chage colloidal paticles with a soft-coe. 3. Simulate the Lennad-Jones potential. M.Boccio, D.Costa, Y.Liu, S.H. Chen, JCP 24, 845 (26)

29 Numeical Solutions 6. Calculate the stuctue facto S(Q): Numeical Solutions to OZ Equation The development of poweful compute Advantage of a numeical methods: Tivial to extend the method to moe complicated potential Easy to extend to all kinds of diffeent closues (HNC, RY, Zeah-Hansen, SCOZA, ) The validity of new methods could be easily veified by compute simulations Relatively easy to implement the themodynamic consistency Application of numeical solution to analyze the scatteing esults of colloidal systems becomes moe and moe impotant. Many Examples! Such as DLVO (HNC), One Yukawa (HNC) (potein solutions) A. Tadieu, S. Finet, and F. Bonnete, J. Cyst. Gowth 232, (2). Two Yukawa (HNC) (potein solutions, micella systems) M.Boccio, D.Costa, Y.Liu, S.H. Chen, JCP 24, 845 (26) C. Caccamo, Integal Equation Theoy Desciption of Phase Equilibia in Classical Fluids, Physics Repot 274, -5 (996). And efeences theein.

30 7. Example : Had Sphee Systems = A P(Q) S(Q) (Assume A=) P(Q) -2-4 R=4Å S(Q) Q (Å - ) Q (Å - ) Volume faction: Ф=4%..5 S(Q) is calculated using PY closue Q (Å - )

31 7. Example : Had Sphee Systems = A P(Q) S(Q) (Assume A=) Ф=% S(Q) Q (Å - ) Q (Å - ) Ф=5% S(Q) Q (Å - ) Q (Å - )

32 .8 7. Example : Had Sphee Systems = A P(Q) S(Q) (Assume A=) Ф=% S(Q) Q (Å - ) Q (Å - ) Ф=2%.5 S(Q) Q (Å - ) Q (Å - )

33 7. Example 2: Shot-ange attaction systems = A P(Q) S(Q) -2 (Assume A=) U ( ) k T B = K e κ ( σ ), (K = -2, κσ = ) P(Q) -4 R=4Å Q (Å - ) P(Q) Had Sphee Volume faction = 3% S(Q) is calculated with the MSA closue Q (Å - )

34 7. Example 2: Shot-ange attaction systems = A P(Q) S(Q) (Assume A=).8.6 P(Q) Had Sphee Ф=% Q (Å - )

35 7. Example 2: Shot-ange attaction systems = A P(Q) S(Q) (Assume A=).8.6 P(Q) Had Sphee Ф=5% Q (Å - )

36 7. Example 2: Shot-ange attaction systems = A P(Q) S(Q) (Assume A=) P(Q) Had Sphee Ф=% Q (Å - )

37 7. Example 2: Shot-ange attaction systems = A P(Q) S(Q) (Assume A=).8.6 P(Q) Had Sphee Ф=2% Q (Å - )

38 7. Example 3: Electostatic epulsion systems = A P(Q) S(Q) (Assume A=) U ( ) k T B = K e κ ( σ ), (K = 2, κσ = 4 ) P(Q) -2-4 R=4Å Q (Å - ) P(Q) Had Sphee Volume faction = 3% S(Q) is calculated with the MSA closue Q (Å - )

39 7. Example 2: Electostatic epulsion systems = A P(Q) S(Q) (Assume A=) P(Q) Had Sphee Ф=%.2-2 Q (Å - - )

40 7. Example 2: Electostatic epulsion systems = A P(Q) S(Q) (Assume A=) P(Q) Had Sphee Ф=5%.2-2 Q (Å - - )

41 7. Example 2: Electostatic epulsion systems = A P(Q) S(Q) (Assume A=).8.6 P(Q) Had Sphee Ф=% Q (Å - )

42 7. Example 2: Electostatic epulsion systems = A P(Q) S(Q) (Assume A=).8.6 P(Q) Had Sphee Ф=2% Q (Å - )

43 7. Example 2: Electostatic epulsion systems = A P(Q) S(Q) (Assume A=) Ф=%.8 P(Q) Had Sphee.8 P(Q) Had Sphee Q (Å - ) -2 - Q (Å - ) U ( ) k T B = K e κ ( σ ),(K = 2, κσ = 4 ) U ( ) k T B = K e κ ( σ ), (K = 2, κσ =.5 )

44 7. Example 2: Electostatic epulsion systems = A P(Q) S(Q) (Assume A=) Ф=.5% Ф=.%.8 P(Q) Had Sphee.8 P(Q) Had Sphee Q (Å - ) -2 - Q (Å - ) U ( ) k T B = K e κ ( σ ), (K = 2, κσ =.5 )

45 7. Example 3: Electostatic epulsion systems with shot-ange attaction = A P(Q) S(Q) (Assume A=) -2 R=4Å P(Q) Had Sphee Q (Å - ) Volume faction = 3% S(Q) is calculated with the MSA closue.

46 7. Example 3: Electostatic epulsion systems with shot-ange attaction = A P(Q) S(Q) (Assume A=) Ф=% Ф=5%.8 P(Q) Had Sphee.8 P(Q) Had Sphee Q (Å - ) -2 - Q (Å - )

47 7. Example 3: Electostatic epulsion systems with shot-ange attaction = A P(Q) S(Q) (Assume A=) Ф=%.8.6 P(Q) Had Sphee S(Q) Q (Å - ) Q (Å - )

48 7. Example 3: Electostatic epulsion systems with shot-ange attaction = A P(Q) S(Q) (Assume A=) Ф=2%.8.6 P(Q) Had Sphee S(Q) Q (Å - ) Q (Å - )

49 P(Q) Had Sphee 7. Example 3: Electostatic epulsion systems with shot-ange attaction = A P(Q) S(Q) Ф=5% (Assume A=) S(Q) Q (Å - ) Q (Å - ) K =, Z =2, K 2 =.25, Z 2 =.5

50 8. Relations with othe methods: Light scatteing Obtain the second viial coefficient, B 22, using static light scatteing: 2 k T B22 M wn A = 2π ( g( ) ) d = 2π ( e ) U ( ) Velev et al., Biophysical Jounal 75, 2682 (998) B 2 d lysozyme

51 8. Summay and β-appoximation = A P(Q) S(Q) Decoupling appoximation: one component system with spheical paticles Given the know infomation of inte-paticle potential, S(Q) can be obtained by solving OZ equation: isotopic inteaction Big touble! Disks, ods, paticles with lage polydispesity Anisotopic inteactions

52 8. Summay and β-appoximation = A P(Q) S(Q) When polydispesity is small o the colloidal paticle is close to a spheical shape β-appoximation = can be appoximated with one component stuctue facto. S.-H. Chen Ann. Rev. Phy. Chem

53 8. Available esouces. Available compute codes SANS & USANS Analysis with IGOR Po Many fom facto models The stuctue facto fo had sphee system (PY), sticky had sphee system (PY), the Hayte-Penfold method (MSA fo one Yukawa had sphee system). Stuctue facto fo two Yukawa had sphee system with Matlab codes MSA closue. Feely available by contacting Yun Liu o Sow-Hsin Chen 2. Website lectue notes and tutoials NCNR SANS Tutoial Lectues by Roge Pynn