Response of Soft Continuous Structures and Topological Defects to a Temperature Gradient Statmech Journal Club Talk Vinay Vaibhav February 12, 2018 Rei Kurita, Shun Mitsui, and Hajime Tanaka; Phys. Rev. Lett. 119, 108003 (2017) 

What is the response of soft continuous structures to a temperature gradient? 

Motivation Ludwig-Soret effect: Migration of fluid particles in a binary liquid mixture under a temperature gradient; well studied problem Response to temperature gradient: Polymer solutions, protein solutions, DNA solutions, colloidal suspensions, liquid mixtures No study: Response to a temperature gradient of soft continuous structures coexisting with a liquid (gels, membranes etc) Biological importance: Effect of inhomogeneous temperature field on the lateral diffusion of proteins or molecules on a membrane 

Experimental study of the response to a temperature gradient of a stacked membrane system, homeotropically aligned between two parallel glass plates In this paper 

Membrane System Lyotropic liquid crystal: Mixture of surfactant (amphiphilic) molecule C10 E3 (tri-ethyleneglycol mono n-decyl ether) and water Phase transition between lamellar and sponge phase: Weakly first order (order-disorder), nucleation Lamellar phase: Stabilised by entropic repulsions (Helfrich interaction) L : Lamellar phase, Ordered, Smectic order L3 : Sponge phase, Isotropic, Disordered ↵ Image: Yasutaka Iwashita & Hajime Tanaka; Nature Materials volume 5,147–152 (2006) 

In phase separation region three characteristic morphologies were observed depending on heating rate and concentration Network pattern (a): Rapidly heating a lamellar phase in coexistence region (major sponge), lamellar phase shrinks and forms a transient network structure, nucleation and growth of sponge phase Droplet pattern (b): Network structure coarsens, lamellar phase shrinks to its equilibrium volume fraction Cellular Pattern (c): Slower heating of lamellar phase forms a stable cellular structure composed of a lamellar cell wall, lamellar phase interconnected but sponge phase isolated in each compartment (d): Pattern evolved from (c) on heating DPS (e) : For very slow heating rate, the sponge phase (minority phase) forms isolated droplets (f): Pattern evolved from (e) on heating Image: Yasutaka Iwashita & Hajime Tanaka; Nature Materials volume 5,147–152 (2006) 

Image: Yasutaka Iwashita & Hajime Tanaka; Phys. Rev. Lett. 95, 047801 (2005) (a) Striped pattern (b) Disordered mosaic pattern (c) Onion pattern Various organisations of lamellar phase formed in the wedge cell 

Why this system? Large characteristic length scale and slow dynamics of the system enable real-time optical microscopy observation of the ordering process under the influence of confinement 

Experimental Setup Sample sandwiched between two parallel glass plates Concentration measurement: Fluorescent dye molecules (rhodamine 6G) are put, perfectly attached to membranes Confirmed that the decay rate of intensity of dye molecules is independent of the location and spatially homogeneous if whole sample is in same temperature Image: Rei Kurita, Shun Mitsui, and Hajime Tanaka; Phys. Rev. Lett. 119, 108003 (2017) (Supplemental material) 

Temperature protocols used in the experiment Equilibrate the system (for 12 wt%) in the sponge phase at 38o C Cool the system with very slow cooling rate of 0.01 K/min to 27oC, induces spontaneous formation of homeotropically aligned lamellar phase, membranes are aligned in parallel to glass substrates Anneal the sample over 24 hours Applying temperature gradient: Change the temperature of one of the two stages while keeping the temperature of other stage fixed — Heat left stage from 27oC to 34oC with a heating rate of 1K/min at t = 0, keeping the right stage at 27oC — At this concentration, lamellar phase is stable between 10oC and 36oC System observed for 1500 minutes for the three regions HT, TG and LT HT: Region on the high-temperature stage TG: Region between the two stages under the temperature gradient LT: Region on the low-temperature stage 

Relaxation dynamics: Cool the left stage from 34oC to 27oC at t = 1800 min with a cooling rate of 1 K/min, temperature gradient removed Observation: Decay of I(t) is slower in the HT region than in the LT region, opposite to the response of system to the temperature gradient Image: Rei Kurita, Shun Mitsui, and Hajime Tanaka; Phys. Rev. Lett. 119, 108003 (2017) 

Four possibilities (i) Temperature gradient induced change in the degree of membrane undulation fluctuation — Larger membrane fluctuation in the LT region than in the HT region — Temperature gradient causes left-right imbalance: net lateral force towards low temperature direction — Migration of membrane towards the LT side, enhancement of out-of-plane membrane fluctuation (ii) Larger membrane fluctuations at a lower local temperature — The amplitude of fluctuations decreases with an increase in temperature due to an unusual temperature dependence of bending elasticity (iii) Change in the lateral area of surfactant molecules — Lateral area may be larger in the HT region than in the LT region (iv) Increase in the number of membranes in the LT region (iii) and (iv) are not possible: — (iii): Slow intensity change not consistent with a quick response expected for a molecular scale change — (iv): Requires formation of new edge dislocations; energetically too costly  

Possibility (ii) Bending modulus and layer compression modulus B can be a function of T and/or To clarify the dependence of B on and/or , consider a new experiment focusing on the motion of edge dislocations in the lamellar phase confined in a wedge-shaped cell  rT  rT Equilibrate the system (for 7 wt%) in the sponge phase at 36o C Cool the system with very slow cooling rate of 0.01 K/min to 25oC, induces spontaneous formation of homeotropically aligned lamellar phase Anneal the sample over 24 hours Applying temperature gradient: Change the temperature of one of the two stages while keeping the temperature of other stage fixed — Heat left stage from 25oC to 32oC with a heating rate of 1K/min at t = 0, keeping the right stage at 25oC Observe the temporal change of the edge dislocation array in TG region Temperature protocols used in the experiment 

Image: Rei Kurita, Shun Mitsui, and Hajime Tanaka; Phys. Rev. Lett. 119, 108003 (2017) (Supplemental material) 

Edge dislocations have larger moving distances s near hotter stage, move opposite direction near colder stage (even temperature of colder stage is unchanged) Edge dislocation do not move when temperature is uniformly changed from 25oC to 32oC The ratio /B is independent of T, possibility (ii) ruled out Image: Rei Kurita, Shun Mitsui, and Hajime Tanaka; Phys. Rev. Lett. 119, 108003 (2017) Yasutaka Iwashita and Hajime Tanaka Phys. Rev. E 77, 041706 (2008)  i = ( 12w Btan✓ )1/3s1/3 i w /  d Edge dislocation, membrane fluctuation, layer compression modulus B Cell thickness gradient, layer compression energy Formation of edge dislocation: relax the layer compression energy 

Further confirmation to possibility (i) Investigate the phase transition behaviour from the lamellar phase to sponge phase Apply temperature gradient to lamellar phase for 1440 min and then set both stage at same temperature Heat whole system gradually with a heating rate 0.1 K/min Transformation to sponge phase take place early in LT region — Membrane undulation fluctuation is larger in LT region than HT region Thermal forcing transports the membrane towards LT side under the constraint, leads to excess surface area of membrane, increase of out of plane membrane fluctuation in LT side, local layer compression modulus B becomes larger, responsible for tilting of edge dislocation Reason 

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