View source for Temperature-controlled transitions between glass, liquid and gel states in dense p-NIPA suspensions

''Written by Kevin Tian, AP 225, Fall 2011''

--[[User:Ktian|Ktian]] 07:32, 25 September 2011 (UTC)

'''Title:''' Temperature-controlled transitions between glass, liquid and gel states in dense p-NIPA suspensions

'''Authors:'''  Giovanni Romeo, Alberto Fernandez-Nieves, Hans M. Wyss, Domenico Acierno, and David A. Weitz

'''Journal:''' Advanced Materials - Special Issue: Stimuli-Sensitive Polymers, Volume 22, Issue 31, pages 3441–3445, August 17, 2010

'''Keywords:''' [[phase transition]], [[elasticity]], [[polymers]], [[viscoelasticity]], [[polymer solution]]

==Paper Summary==

Although elastic behaviors in of themselves are rather well studied, there are several materials that exhibit interesting characteristics with microgels being one of them.  Microgels are essentially polymers that have been chemically cross-linked to form particles in a gel that are colloidal in size.  As with their macroscopic counterparts, the microgel can be swollen via introduction of a solvent.  However what distinguishes microgels from other gels is that one can manipulate the degree of swelling by only external stimuli (such as temperature).

Poly-N-isopropylacrylamide (p-NIPA) is the microgel studied in this paper.  It is interesting since it's lower critical solution temperature (LCST) is 33<math>\deg C</math>.  A curious property of p-NIPA is that one is capable of causing tempeature controlled transitions between three states (glass, liquid and gel).  These three states can be easily distinguished by observing the mechanical properties of the system under various conditions.

This paper essentially describes the process through which the authors identified and verified the transitions, analyzed the behaviors of the system at the transition points and briefly discussed potential microscopic origins of the system.


==Experiment==
'''Basic Setup'''

The authors used temperature- and pH-responsive particles consisting of p-NIPA copolymerized with ~5% acrylic acid , cross-linked with 0.5% N,N'-methylenebisacrylamide.  In order to determine the range of temperatures of concern (specifically the approximate LCST temperature) differential scanning calorimetry (DSC) was utilized to find an edothermic peak.  For the p-NIPA microgel described the LCST was found to lie in the range of 29-31 <math>\deg C</math> while holding the suspension at pH = 3.

Several parameters are defined as follows:
*The particle number concentration, ''n''
*The volume of the particle measured under dilute suspension condition (limit of ''n'' going to 0), V
*The average polymer mass per particle, <math>m_p</math>
**This quantity is known to depend on the temperature, thus <math>V = V(T)</math>
*The generalized packing fraction, <math>\xi = n V</math>
**This quantity is known to depend on the temperature, thus <math>\xi = \xi (T)</math>
*The linear viscoelastic moduli <math>G'</math> and <math>G''</math>.
**G' is the elastic modulus
**G'' is the viscous modulus
**These quantities are known to depend on the temperature and frequency of applied strain, thus <math>G' = G'(T,\omega), G'' = G''(T,\omega)</math>
*Polymer weight fraction, <math>w_t</math>
*Intrinsic volume fraction, <math>k = {\xi \over {w_t}} = {V \over m_p}</math>
**This is true since solution density is near identical to water

The temperature dependence of particle volume is determined by performing dynamic light scattering (DLS).  Determining the temperature dependence of the volume fraction is done by using an Ubbelohde tube.  The results of this are in Figure 1a.

Determining the temperature dependence of the linear elastic moduli of the suspension is obtained by fixing frequency and strain applied to the sample and slowly varying T.  The results of this are in Figure 1b.

The frequency dependence of  <math>G'</math> and <math>G''</math> was also observed in order to characterize the relaxation dynamics of the three microgel phases.

==Results==

[[Image:kt-4-fig1.jpg|thumb||left|200px|Figure 1.  Taken from article.  Generally the x-axis is Temperature, T, and the y axes are for a) <math>k = \Box, V = \bigcirc</math>, and b) <math>G' = \bullet, G'' =\bigcirc , \xi = \star</math>]]
It is noted that due to the fact that the solution density is essentially that of water, ''k'' and ''V'' should have the same temperature dependence, and are linearly inter-related.  This can be observed in Figure 1a, where the an additional plot of ''k'' vs ''V'' is given to demonstrate the linearity.  

A typical response of the G', G'', and <math>\xi</math> measurements is given in Figure 1b.  Here we can observe that there are regions where one modulus dominates over the other.  In the region of <math> T < 26^\circ C</math> we notice that the elastic modulus (G') dominates over the viscous modulus (G'').  As temperature is increase the difference progressively smaller, suggesting solidlike behaviors.  This in addition to the absence of visible Bragg peaks indicates the transition to a glass like state has occurred.

At <math> T ~ 28^\circ C</math> we notice that G' < G'', which is indicative of liquid-like behaviors.  however the particule volume fraction <math>\xi</math> is rather high, corresponding more to a random close packing.

As the temperature is further increased the interactions between p-NIPA microgel particles transitions from repulsive to attractive (a well known phenomenon).  The LCST is thus identified to definitively be the temperature at which both G' and G'' are at a minimum ( <math> T = 29^\circ C</math>).  We notice however that immediately after the LCST temperature there is a very sharp increase in G' and G''.  This may be attributed to the formation of a volume-spanning colloidal gel.  Thus over the range of temperatures displayed in Figure 1, there is evidence of a phase transition of the microgel from a Glass (at lower temperatures) to a Liquid (at temperatures near but below the LCST) and to finally a gel (at temperatures above the LCST).


[[Image:kt-4-fig2.jpg|thumb|200px|Figure 2.  Taken from article.  Plotted is the frequency dependence of the microgel's linear viscoelastic moduli at the a) glassy state, b) liquid-like state, and c) gel-like state at varying temperatures.]]

In order to examine the relaxation dynamics of the microgel system in its various phases the frequency dependence of the viscoelastic moduli was analyzed (including the variation of these dependencies with respect to temperature).  The results of this are displayed in Figure 2, for the 3 phases glassy, liquid- and gel-like corresponding to plots a), b), and c).

For the 'glassy' phase it was noticed that there was a frequency-independent plateau in G' and a minimum in G'' at lower temperatures, both typical features of a glassy system.  Additionally the increase of G'' with decreasing <math>\omega</math> before the marked minimum serves to support the identification of the phase as a glass.  The authors thus concluded that the system behaved in a manner resembling glassy hard sphere suspensions, however due to the difference in the systems, this response cannot possibly be of the same origin as this analogous system.

For the 'liquid-like' phase there are two distinct regions of different suspension dynamics.  At the lower temperatures (below <math>25^\circ C</math>) it was noticed that the plots seemed to suggest that the particles had begun to de-swell after a reaching a high enough packing fraction.  This is due to their finite osmotic compressibility, thus allowing for significantly higher packing than is normal for this phase.  At higher temperatures G' and G'' both begin to exhibit strong frequency dependence, which in the upper bound of <math>28^\circ C</math> tends towards the terminal behavior of a viscoelastic liquid, thus the remark that this phase corresponds to a liquid-like state.

Once the system is above the LCST there is again another change in the frequency dependence of the system, which can also be observed in the viscoelastic moduli.  Both G' and G'' are characterized by a power law of type <math>G ~ \omega^{0.3}</math> in the entire frequency range.  This power law relation with respect to frequency is characteristic of transient particle networks.  However the exact mechanism by which these networks form is undetermined.  One proposition is that these networks form via the crowding of stable clusters that formed from the attractive potential of the polymers, thus allowing gelation to occur.  However further experiments must be performed to verify this.


[[Image:kt-4-fig3.jpg|thumb|200px|Figure 3.  Taken from article.  The temperature dependence of <math>G'_p</math> for two different variations at two polymer concentrations.  a) Temperature, and b) <math>\xi</math>.]]
The presence of liquid-like behavior was most unexpected around the LCST, and eve more so that concentrations <math>\xi</math> can be attained for this phase well above random close packing (contrasting this microgel further from the hard sphere model).  It was proposed that the repulsive softening of the particles as T nears the LCST may have a role to play in the mechanical response of the system.  In order to determine the behavior of the elastic plateau modulus, G'_p was plotted as a function of temperature around the LCST.  This is shown in Figure 3.

==Conclusions==

As it has been shown above, concentrated suspensions of these p-NIPA microgel particles can undergo transitions between glassy, liquid- and gel-like behaviors as the temperature of the particles is varied around the LCST.  Also it was determined that viscoelastic response is determined by both effective particle volume fraction and effective interparticle potential.  Behaviors that were not expected include the discovery that mid-transition between glassy and liquid states the generalized volume fraction, even <math></math>, is orders of magnitude too small for a hard-sphere model.  This suggests the temperature is doing more than simply altering the suspension volume fraction; however the details of this effect are speculation at best.

Interestingly enough this qualitative behavior is not necessarily limited to the just this particular suspension but to all polymer microgel suspensions.  It is believed that this study brings about merely one of a whole class of materials that likely have very similar behaviors, much of which is not very well understood.  This is reflected in the fact that much of the discussions regarding explanations for the behaviors are possibilities rather than definitive solutions.  The interactions of these cross-linked polymer gels suggests there is far more to be researched regarding the microscopic origins of the elastic properties of microgels across temperature ranges.