Mechanics from Calorimetry: Probing the elasticity Elasticity for ResponsiveHydrogels

Frank J. Aangenendt,1, 2, 3 Johan Mattsson,4 Wouter G. Ellenbroek,2, 5 and Hans M. Wyss1, 2, 3, ∗

1Dutch Polymer Institute (DPI), P.O. Box 902, 5600AX Eindhoven, The Netherlands2Institute for Complex Molecular Systems, Eindhoven University of Technology,

P.O. Box 513, 5600MB Eindhoven, The Netherlands3Department of Mechanical Engineering, Materials Technology,

Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands4School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, U.K.

5Department of Physics, Eindhoven University of Technology,P.O. Box 513, 5600MB Eindhoven, The Netherlands

(Dated: September 10, 2018)

Temperature-sensitive hydrogels based on polymers such as poly(N -isopropylacrylamide) (PNIPAM)undergo a volume phase transition in response to changes in temperature. During this transition,distinct changes in both thermal and mechanical properties are observed. Here we illustrate andexploit the inherent thermodynamic link between thermal and mechanical properties by showingthat the compressive elastic modulus of PNIPAM hydrogels can be probed using differential scanningcalorimetry. We validate our approach by using conventional osmotic compression tests. Our methodcould be particularly valuable for determining the mechanical response of thermosensitive submicron-sized and/or oddly shaped particles, to which standard methods are not readily applicable.

PACS numbers:

I. INTRODUCTION

Stimuli-responsive hydrogels respond to changes intheir physical and chemical environment. The proper-ties of these materials, including their volume and theirmechanical response, can be reversibly controlled by ex-ternal stimuli such as pH, ionic concentration, tempera-ture or electric fields [1–5]. Typical examples of this classof materials are hydrogels or microgels made from thepolymer poly(N -isopropylacrylamide) (PNIPAM), whichexhibits a lower critical solution temperature (LCST) ataround 32C. Near the LCST, a temperature variationof merely a few degrees can lead to a change in volumeby more than an order of magnitude [2–4]. Such a dra-matic response to external stimuli can be exploited inapplications including stimuli-responsive surfaces [6], softvalves [7], and responsive materials for drug delivery sys-tems [5]. The change in volume is only one manifestationof the alterations in the physical state of the system as thetemperature is increased across the LCST; the thermaland mechanical properties of the material also undergosignificant changes.

The associated changes in thermal properties have beenwidely investigated in PNIPAM solutions and networksusing differential scanning calorimetry (DSC) [8, 9]. Typ-ically, a pronounced endothermic peak correspondingto the LCST is observed in the heat flow. For PNI-

∗Electronic address: H.M.Wyss@tue.nl

PAM microgels, alterations of the mechanical propertieshave been investigated using multiple techniques, includ-ing conventional mechanical compression tests [10], os-motic compression measurements [11, 12], atomic forcemicroscopy [13], and Capillary Micromechanics [14–16].For materials that can be considered elastically homoge-neous, Capillary Micromechanics provides experimentalaccess to both the elastic shear modulus G and the com-pressive elastic modulus K, thus quantifying the full elas-tic behavior of the material, including the Poisson’s ratioν. Using this technique on PNIPAM microgels, a pro-nounced dip in the Poisson’s ratio was observed aroundthe LCST of these microgels [16], in agreement with pre-vious measurements on macroscopic PNIPAM hydrogelsby Hirotsu [17], where an even more dramatic dip wasobserved. This dip is due to a reduction of the compres-sive modulus K relative to the shear modulus G, whichcan be rationalized by considering that the large thermalexpansion coefficient near the LCST should intuitivelygo hand in hand with a large compressibility; the argu-ment being that volumetric changes, whether thermallyor mechanically induced, are less energetically costly inthis temperature range. This example illustrates the in-herent connection between the thermal and mechanicalbehavior of these materials.

Indeed, knowledge of the mechanical properties of re-sponsive materials is often of key importance for gaininga detailed understanding of their behavior. Examples in-clude responsive hydrogels used in targeted drug delivery,responsive surfaces, or responsive valves in microfluidicsystems. A detailed understanding of the mechanical be-havior of such responsive materials is also highly relevantto the design of materials in the promising field of shape-morphing materials, where mechanical instabilities are

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exploited to achieve highly controlled, complex shapesbased on relatively simple structures [18].

However, the inherent link between thermal and me-chanical properties has not been exploited to extract me-chanical properties directly from calorimetric measure-ments. Such an approach would be especially valuablefor sub-micron or oddly shaped temperature-responsiveobjects such as microgels, and hydrogel particles, and,potentially, for temperature-sensitive biological materialsas well. For all of these materials mechanical propertiesare difficult to measure using traditional techniques.

In this paper, we show that compressive elastic modulican be probed using DSC measurements, without directlymeasuring any forces or stresses. To do so, we exploit theinherent thermodynamic link between calorimetric andmechanical material properties of temperature-sensitivehydrogels. We use macroscopic PNIPAM hydrogels asa model material to test our calorimetry-based measure-ment method. To validate our approach, we compare theresults to traditional osmotic compression measurementson the same samples, finding good agreement.

II. MATERIALS AND METHODS

PNIPAM hydrogels are synthesized by mixing 40mL of Milli-Q water (resistivity> 18 MΩcm) with 5 wt%NIPAM (N-isopropylacrylamide, Sigma Aldrich), 0.25wt% of the cross-linker (Methylene bisacrylamide, SigmaAldrich ) and 0.1 wt% of the photo-initiator (Irgacure,Sigma Aldrich), corresponding to a monomer-to-cross-linker weight ratio of 100:5. After shaking, we transferthe solution to a well plate (2 mL, VWR) and place itunder a UV lamp (Vilber-Lourmat, model VL215.LC,60W), distance of approximately 9 cm) for 1h, whichresults in the formation of a cross-linked PNIPAM gelnetwork. The resulting hydrogels are cut into a fewpieces, which constitute the individual samples we workwith in all further experiments. These samples are thenplaced in deionized water and allowed to swell overnight.The equilibrium volume of each piece of hydrogel isdetermined by removing the individual sample from thewater bath, removing any extra water from its surface,and weighing it on a balance. In calculating the samplevolume from this weight, we assume the sample’s densityto be equal to that of water.

DSC measurements, are performed on single,millimeter-sized, pieces of hydrogel in different states ofhydration. We prepare these samples by adding differentamounts of deionized water to a single dried piece of hy-drogel, which subsequently swells up to incorporate alladded water. This swelling process takes up to 30s. Ineach series of measurements, we thus use a single piece ofhydrogel to scan a range of different concentrations, fromhighly compressed to fully swollen. The thermodynamicresponses are studied using a heat flux differential scan-ning calorimeter (Q2000, TA instruments). The temper-

ature is increased from 10C to 55C at a rate of 0.125C/min, in analogy to previous work on pNIPAM [19]. Thetemperature is held at 55C for 10 min. Subsequently,the sample is cooled down to 10C using the same rate.Again, the sample is held at this temperature for 10 min,after which the whole procedure is repeated once.

To test whether our heating rates ensure that thesample remains close to its equilibrium state at eachtemperature, we perform measurements also at 0.08 and0.3 C/min, (see the Supplemental Material [21]). Theresults are indeed consistent with the 0.125 C/minexperiments, particularly when comparing the total areaunder the heat capacity peak, rather than its shape. Itis important to note that, in our experiments, we areinterested only in the total heat required to increase thesample’s temperature from T0 to Tf , i.e. the area underthe heat capacity peak.

Osmotic compression is a well-established methodfor characterizing the mechanical properties of hydro-gel samples [20]. We employ it here for validation ofour DSC method. In the osmotic compression method,changes in gel volume in response to an applied externalosmotic pressure Πext are measured, yielding the com-pressive modulus K of the gel [20, 22]. To perform suchmeasurements, we place our hydrogel samples into dialy-sis tubes (VWR) and submerge them in dextran solutions(Mw = 70 kg/mol, from Leuconostoc, Sigma-Aldrich),with concentrations ranging from 3.5 to 18 wt%, corre-sponding to osmotic pressures between 2.28 and 62.5 kPa[20, 23, 24]. We then allow the gels to equilibrate for aperiod of one week in the dextran solutions, after whichtheir final equilibrium weight is measured. From thesedata, we extract the equilibrium volumes as a functionof the applied osmotic pressure, V (Πext). Because thestarting weight of PNIPAM is known, the volume canbe calculated based on the density of water and the PNI-PAM polymer, which are 1 g/cm3 and 1.1 g/cm3, respec-tively.

III. RESULTS AND DISCUSSION

Our method is based on the comparison of the heatrequired to cross the LCST, between a fully swollen hy-drogel and a gel in a compressed state. Since the geldoes not perform work on its environment during theDSC measurement, this heat is equal to the change ininternal energy. As is illustrated in Fig. 1, the differencein internal energy between two different states of swellingat a temperature T0 can be obtained as the difference inheat required to thermally deswell both samples.

Performing these experiments for a range of swellingstates provides the internal energy as a function of com-pression at the temperature T0, which we use to extractthe mechanical properties of the gel at this temperature.

To compare data for gels of different water content,we first subtract the background contribution from the

3

water. To do so, for each data, set we draw a line fromthe heat capacity value at T=20C to T=55C, which werefer to as the straight baseline. We subtract this baselinefrom the data, resulting in corrected heat capacity curves.By calculating the area under the corrected heat capacitydata, the change in internal energy required to increasethe temperature of the sample from its initial to its finaltemperature is determined, as shown in Fig. 1B. The dataare further normalized by the sample dry weight so thatthe results for all samples can be directly compared (seethe Supplemental Material [21] for more details).

We define the normalized change in internal energy ofa fully swollen piece of hydrogel, upon heating from T0

to Tf , as ∆UV0→Vf. As shown in Fig. 1, such a gel also

undergoes a volume change from V0 to Vf . Compressing afully swollen gel piece from V0 to V at constant tempera-ture is associated with a change in internal energy ∆UT0

.Starting from this compressed state, heating the hydro-gel from T0 to Tf is associated with a change in internalenergy ∆UV→Vf

. In both cases, the initially fully swollengel, at volume V0 and temperature T0, reaches the samefinal state, volume Vf at temperature Tf ; therefore, wecan write ∆UV0→Vf

= ∆UT0+ ∆UV→Vf

.In further analysis, we approximate the mechanical

work required to compress the hydrogel at constant tem-perature as WDSC ≈ ∆UT0

, assuming that any heat flowsthat would occur during an isothermal compression aresmall compared to the total difference in internal en-ergy between the compressed and uncompressed states.A similar assumption is commonly made in macroscopicmechanical tests, where temperature changes of the sam-ple associated with compression are generally ignored.We also assume that the entropic contribution is rela-tively small because we cross-linked our hydrogels at aconcentration close to the fully swollen state; entropic ef-fects due to chain stretching are therefore not expected toplay an important role. Under these assumptions, if wemeasure the difference between ∆UV0→Vf

and ∆UV→Vf,

for different compression states, we obtain a good esti-mate of the associate work W needed to compress thegel. This estimated work yields a direct measure of the

material’s compressive elastic modulus, K = −V ∂2W∂V 2 .

Calculating K involves taking a double derivative;therefore, in order to avoid the amplification of exper-imental errors, we wish to describe the DSC data usinga simple and continuous functional form. To arrive at aphysically motivated expression, we take the integral of

a pressure function, W =∫ V

V0Πext(V ) dV , where Πext(V )

is the applied pressure as a function of volume V . Toapproximate this pressure function we follow the stan-dard scaling arguments for the equilibrium swelling ofgels [25], equating the osmotic pressure difference be-tween a semidilute polymer solution and the externalpressure, Πext(V ), with the elastic modulus of a gel as

Πext = β

(V

V0

)−9/4

− β

(V

V0

)−1/3

. (1)

Temperature [°C]

Nor

mal

ized

Hea

t Cap

acity

[J/(K

g)]

Temperature

Volu

me

UT0

UV0!Vf

UV !Vf

A

BUT0

UV0!Vf

UV !Vf

FIG. 1: Extracting mechanical properties from calorimetry.A) Schematic phase diagram of calorimetric measurements.Energies of ∆UV0→Vf and ∆UV→Vf , for the uncompressed andcompressed state, respectively, are required to heat the samplefrom an initial temperature T0 to a final temperature Tf . Weassume that the energy difference ∆UT0 is the work requiredto compress a particle from V0 to V at a constant temper-ature T0. Under this assumption, a measurement of ∆UT0

thus constitutes a mechanical measurement of the compres-sive modulus. B) Typical corresponding calorimetry mea-surements. Excess heat capacity per gram of PNIPAM as afunction of temperature for (lower curve) compressed and a(higher curve) fully swollen sample; a flat level of heat ca-pacity, dominated by the background water, has been sub-tracted. We observe a clear peak around the LCST for bothsamples. The area under the curves corresponds to the excessenergy required to heat the samples, per gram of PNIPAM.Indeed for the uncompressed sample, we find a higher area(\\-hatched) then for the compressed sample (//-hatched).The energy difference (the grey area) corresponds to the in-ternal energy difference ∆UT0 , which we approximate as themechanical work WDSC required to compress the sample fromV0 to Vf .

Here, V/V0 is the ratio between the compressed vol-ume V and the fully swollen volume V0, the first termon the right-hand side denotes the osmotic pressure of asemidilute polymer solution, and the second term repre-sents the elastic modulus according to rubber elasticity.We treat the prefactors as fitting parameters, and, be-cause V = V0 at Πext = 0, the two prefactors must be

4

identical, leaving a single fitting parameter β.We obtain W by integrating the applied pressure Πext

over the volume as

W =4β

5

( VV0

)−5/4

− 3β

2

( VV0

)2/3

+ 0.7β , (2)

where we have added the term 0.7β to comply with theboundary condition W = 0 at V = V0. Using DSC, wedetermined the difference in changes of internal energy(or the work WDSC) for hydrogels of different dry weightand at different degrees of compression (V/V0). Becausethe concentration of PNIPAM is known at every rehy-dration step, V and V0 can be calculated based on thedensity of water and PNIPAM, 1.1 g/cm

3and 1 g/cm

3,

respectively.The experimental DSC results are plotted as red tri-

angles in Fig. 2A and the corresponding fit to the exper-imental data is shown as a solid line. We see that theexperimental data clearly follows the dominant power-law term with exponent −5/4 from Eq. (2), within mostof the fitting range, as indicated by the dotted line.This agreement demonstrates that our choice for thefunctional form of Πext is appropriate. Thus, in ourapproach, the compressive modulus K can be deter-mined directly from WDSC, via a double derivative, as

K(V ) = −V ∂Πext

∂V = −V ∂2WDSC

∂V 2 , shown in Fig. 2B as thesolid line. In the swollen state, at V = V0, we obtainK ≈ 6.3 ± 1.43 kPa.

It is important to note that, in our experiments, weare interested only in the total energy required to heatthe sample from T0 to Tf , i.e., the area under the heatcapacity curve. Thus, as long as we compare experimentsperformed at the same heating rate, any rate-dependentsmearing of the heat capacity peak would be relativelyinconsequential. We show in the Supplemental Mate-rial [21] that, for heating rates of 0.08 and 0.3 C/min,we indeed obtain a similar result as for the 0.125 C/minexperiments.

To verify our DSC-based method, we perform conven-tional osmotic compression experiments. By doing so,we can verify our chosen pressure function, the result-ing energy function, and our assumption that WDSC ≈∆UT0

. The experimental results are plotted as opencircles in Fig. 3 and the fit using Eq. (1) is depictedas the dashed line. The volume-dependent compressivemodulus K(V ) can be determined from its definition,K (V ) = − (V/V0) ∂Πext

∂(V/V0) , and, finally Wosm can be de-

termined by applying Eq. (2). The results are shown asthe dashed lines in Fig. 2A and 2B. Using this approxima-tion for the pressure function, we extract a compressivemodulus as a function of V/V0. At the equilibrium vol-ume, we obtain K(V0) ≈ 4.6 ± 0.52 kPa, in good agree-ment with the K ≈ 6.3 ± 1.32 kPa value obtainedvia the DSC method. The uncertainties associated withboth methods are estimated in a separate error analysis,included in the Supplemental Material [21].

102

104

106

10-1 100103

104

105

106

A

B

DSC error bar|__

FIG. 2: A) Work W required to compress a particle from V0

to V as a function of the volume ratio V/V0. The red trian-gles are the calorimetric results (∆UT0) and the solid line isthe fit using Eq. (2), resulting in β ≈ 3.29 kPa. This fit isin good agreement with the prediction based on the osmoticcompression measurement (Wosm), plotted as a dashed line.The dotted line indicates a slope of −5/4 which is the domi-nant term in Eq. (2). The average error for DSC experimentsis 10 %, as indicated by the error bar in the bottom-left cor-ner. B) Corresponding compressive modulus K as a functionof V/V0. At V = V0, we find K = 6.32 ± 1.43 kPa and4.59 ± 0.52 kPa based on DSC (the solid line) and osmoticcompression (the dashed line), respectively.

0.2 0.4 0.6 0.8 1

Normalized Volume V/V0

0

20

40

60

80

Osm

otic

Pressure

Πext[kPa]

FIG. 3: Osmotic pressure as a function of the normalizedhydrogel volume V/V0. The red circles are the experimentaldata from the osmotic compression tests and the dashed lineis a fit to Eq.(1), with β=2.39 ± 0.06 kPa. The error bars aresmaller than 1%, which is smaller than the marker size; seethe error analysis in the Supplemental Material [21].

5

The comparable results for WDSC and Wosm clearlyindicate that the two completely different experimentalapproaches lead to consistent results, thereby confirmingthe validity of our DSC-based approach and our assump-tion of WDSC ≈ ∆UT0

. The good agreement between thetwo measurements thus indicates that, for these materi-als, the mechanical work needed to compress a particlecan be approximated by the difference in internal energybetween the swollen and compressed states, neglectingany heat flows that occur during compression.

However, it is not obvious that this approximation isjustified for all types of temperature-sensitive gel ma-terials. The role of entropy is expected to be largestfor gels that are cross-linked in the collapsed state, asswelling of such gels requires significant stretching ofpolymer chains. However, even in this case, enthalpiceffects should play a major role and constitute a signif-icant fraction of the free energy difference between theswollen and compressed states of the gel.

In our experiments, the gels were cross-linked at roomtemperature, at a concentration near the fully swollenstate of the system. For this case, compressing the ma-terial results in much smaller changes in chain entropy,as the cross-linking points are brought closer togetherwith respect to the equilibrium chain configuration, withno associated stretching of chains. Moreover, compres-sion will result in a reduction of both the mixing entropyand the configurational chain entropy. As a result, forthis case the DSC-based measurement in fact representsa lower bound on the compressive modulus. While we ex-pect our approximation to be justified for various typesof gels and other T -sensitive materials, its validity shouldbe checked by comparison to separate mechanical mea-surements, as we do for the PNIPAM gels used here.

IV. CONCLUSIONS

In this paper, we perform calorimetric measurementson PNIPAM hydrogels at different levels of compressionand show that the change in internal energy requiredto heat a sample at starting temperature T0 to a finaltemperature Tf above its LCST is lower than that foran uncompressed sample that undergoes the same heattreatment. The difference between these two changes ininternal energy must be equal to the difference in in-ternal energy between the initially compressed and the

uncompressed states, respectively. We approximate thisdifference in internal energy as the work W required tocompress the gels at a constant temperature T0, whichin turn yields the compressive (bulk) modulus K. Themost direct justification for the validity of this approx-imation is the good agreement we obtain between theconventional osmotic compression measurements and theDSC-based measurements, as shown in Fig. 2.

To minimize the amplification of experimental errorsintroduced by the derivatives involved, we fit the DSCand osmotic compression data to a physically meaningfulfunctional form and use this approximation to extractelastic moduli.

We note that to achieve accurate measurements of thecompressive modulus, a series of DSC experiments acrossa significant range of concentrations is required. More-over, the heating rate in the DSC experiment should beslow enough to give the gels sufficient time to remainclose to their equilibrium state during (de)swelling. As aresult, the measurements are relatively time consuming.

However, the sample preparation for the DSC exper-iments is straightforward and we expect the methodto be applicable to a wide range of materials that ex-hibit a pronounced volume phase transition. Our resultsdemonstrate that calorimetry can be a powerful tech-nique to probe the mechanical properties of temperature-responsive gels. Importantly, the method does not re-quire the measurement of any stresses or pressures, aswould be required in a traditional mechanical test. Ourmethod can therefore be particularly useful for sub-micron and oddly shaped thermosensitive materials forwhich established methods are inadequate.

Future improvements to our approach, including a bet-ter understanding of the changes in the physical stateof thermosensitive materials during heating, could en-able detailed measurements of the compressive modulusas a function of temperature for a wide range of mate-rials. We expect our approach to be immediately use-ful for the study of temperature-sensitive soft materials,such as those used in smart drug delivery systems, shape-morphing materials, and responsive soft actuators.

We thank Paul van der Schoot for the valuable discus-sions. The work of F.J.A. and H.M.W. forms part of theresearch program of the Dutch Polymer Institute (DPI),Project No. 738; we are grateful for its financial support.J.M. and H.M.W. are also grateful to the Royal Society(Grant No. IE111253) for the financial support.

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7

SUPPLEMENTARY INFORMATION

Literature references below refer to the reference sec-tion of the main paper above.

Appendix A: DSC data analysis

Differential scanning calorimetry (DSC) measurementsare performed on pNIPAM hydrogels prepared from re-hydration of dried gels, as described in Section II. Westudy hydrogels from different batches, each with a dif-ferent pNIPAM dry weight. All measurements are per-formed at a rate of 0.125 C/min within a temperaturerange from T = 10–55 C. The determined differentialheat flux is converted to an apparent heat capacity Cp(T )through division by the imposed heating rate. The ap-parent heat capacity Cp(T ) is plotted for gels prepared indifferent states of hydration in Fig.4. The correspondingstates of compression (in terms of the volume ratio V/V0)and dry weights mpNIPAM are summarized in Table I.

In the temperature range of interest, the heat capacityof water is featureless, and since gels at different degreesof hydration contain different amounts of water, the totalmeasured apparent heat capacity will be shifted along they-axis, as observed in Fig.4.

Thus, to compare data for gels of different water con-tent, we subtract this contribution of to the backgroundwater. To do so, for each data set we draw a straightline from heat the capacity value at T=20C to that atT=55C; we refer to this line as the straight baseline. Wesubtract this baseline from the data, the result is showin Fig. 5.

Moreover, to account for the variation in the pNIPAMdry weight, we calculate the specific heat capacity, c∗p(T ),by normalizing the C∗p (T ) measured for each sample withits dry weight. The resultant specific apparent heat ca-pacities c∗p(T ) are plotted in Fig.6, where the uppermostdata represents the fully swollen hydrogel and the areaunder this curve is ∆UV0→Vf

. By subtracting the dataobtained for each degree of hydration (compression) fromthe data for the fully swollen state, we obtain ∆UT0

, thedifference in internal energy between the swollen state(T0, V0) and the compressed state (T0, V ).

To extract the elastic properties of the sample fromthese data, we then approximate Wdsc ≈ ∆UT0

, whereWdsc is the mechanical work that would be required forthe isothermal compression of a particle at temperatureT0 from an initial volume V0 to a compressed volume V .From this mechanical work Wdsc as a function of V thecompressive modulus of the gels can be determined di-rectly, as discussed in more detail in the main manuscript.

Appendix B: Influence of heating rate

We also investigated the influence of the heating rateon the ∆UV→Vf

. We performed experiments on the samesamples as in table I but now at 0.08 C/min and 0.3C/min and compared these to the 0.125 C/min mea-surements. As can been seen in Fig. 7 this seems not tohave a significant influence, however faster heating rateswhere not tried and it must be noted that this couldinfluence ∆UT0

.

Appendix C: Error Analysis

1. Osmotic Compression Experiments

We apply an osmotic compression by placing the pNI-PAM particles in a dialysis bag and submerging it ina dextran solution. We vary the dextran weight con-centration c between 3.5 and 18 wt%. The correspond-ing applied osmotic pressures Π are calculated, followingBonnet-Gonnet et al. [23], as

Π = 286c+ 87c2 + 5c3 , (C1)

where c is the polymer concentration in wt% and Π isthe osmotic pressure in Pa. Using this functional formfor the dependence of pressure on concentration, we thusestimate the relative error in the applied pressure ∆Π/Πas

∆Π

Π= (

∂Π

∂c∆c)/Π, (C2)

∆Π

Π=

(286 + 87c+ 15c2

)∆c

286c+ 87c2 + 5c3, (C3)

∆Π

Π=

(286 + 87c+ 15c2

)c

286c+ 87c2 + 5c3∆c

c(C4)

where ∆c/c is the error in measuring the weight of thedextran; we estimate this as ∆c/c ≈ 1% for the scale wehave used.

This results in a error between the 0.1% and 0.35 % inthe concentration range of 3.5 to 18 wt%. This error issmaller than the marker size used in Fig. 3 in the maintext. As a result, no visual error bars are included in thisfigure.

Appendix D: Compressive Modulus Calculations

1. osmotic compression experiment

We calculate the compressive (bulk) modulus based onthe osmotic compression experiment as

K = −∂Π

∂VV, (D1)

8

TABLE I: Volume ratios and dry weights for samples and curves shown in Fig.4

Concentration [wt%] Volume ratio V/V0 mpNIPAM [mg]

5 1 26.5

20 0.25 34.6

30 1/6 28.7

40 1/8 28.7

50 1/10 28.7

60 1/12 28.5

70 1/14 34.3

80 1/16 28.5

90 1/18 34.6

100 1/20 35.3

where Π is the osmotic pressure, which we assume followsthe functional form

Π = β

(V

V0

)−9/4

− β

(V

V0

)−1/3

. (D2)

The associated relative error in the modulus can thusbe estimated as

∆K

K=(∂K∂V

∆V +∂K

∂Π∆Π)/K. (D3)

If for the purposes of this error analysis we only con-sider the dominant term (V −9/4) this results in

∆K

K=

∂∂V

(V −9/4

)∆V

V −9/4+

∆P

P,

∆K

K=−94 V

−13/4∆V

V −9/4+ 0

∆K

K= 9/4

∆V

V.

Assuming a relative error for the volume of ∆V/V=0.05,we obtain for the modulus a relative error of ∆K

K ≈11.25%. As a result, at V/V0 = 1 we obtain K =4.6 ± 0.52 kPa for the osmotic compression experiment.

2. DSC experiment

We calculate the compressive modulus based on theDSC experiments as

K = −∂2W

∂V 2V. (D4)

With W being

W =4β

5

( VV0

)−5/4

− 3β

2

( VV0

)2/3

+ 0.7β , (D5)

the relative error we make in this is

∆K

K=

(∂K

∂V∆V +

∂K

∂W∆W

)1

K. (D6)

If for the purposes of this error analysis we only con-sider the dominant term (V −5/4) this results in

∆K

K=

(∂2W∂V 2 + V ∂3W

∂V 3

)∆V

V ∂2W∂V 2

+∆W

W,

∆K

K=

∆V

V+

∂3W∂V 3 ∆V

∂2W∂W 2

+∆W

W,

∆K

K=

∆V

V+

13 ∗ 9/(4 ∗ 4) ∗ V −17/4∆V

9/4 ∗ V −9/4+

∆W

W,

∆K

K= (1 + 13/4)

∆V

V+

∆W

W,

∆K

K= 4.25

∆V

V+

∆W

W.

If we assume ∆V/V=0.05 and ∆WW = 0.1 we obtain

∆KK ≈ 31.25%. Therefore at V/V0 = 1 we obtainK = 6.3 ± 1.43 kPa from the DSC experiment. Includ-ing these errors, the values of Kdsc = 6.3 ± 1.43 andKosm = 4.6±0.52 overlap, thus indicating a validation ofour DSC-based approach by conventional osmotic com-pression measurements.

9

Temperature T [C ]20 25 30 35 40 45 50 55R

awap

parentheatcapacityC

p(T

)[J/

K]

0

0.5

1

1.5

2

2.5

3

3.552030405060708090100

FIG. 4: Raw apparent heat capacity Cp(T ) as a function of temperature for samples with different states of compression andpNIPAM dry weights as listed in Table 1. The legend indicates the pNIPAM concentration in wt%.

10

Temperature T [C ]20 25 30 35 40 45 50 55C

orrected

heatcapacityC

p[J/K

]

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.652030405060708090100

FIG. 5: Corrected heat capacity as function of temperature for samples with different compression rates and pNIPAM dryweight.

11

Temperature T [/C ]20 25 30 35 40 45 50 55N

orm

eliz

edH

eat

Capaci

tyc? p

[J/K

gpN

IPA

M]

-0.5

0

0.5

1

1.5

252030405060708090100

x 104

FIG. 6: Heat capacity normalized with the dry weight of pNIPAM as a function of temperature. The top curve is for theuncompressed particle and the lower curves are for the pNIPAM gel pieces in different states of compression. The difference inarea between the top curve and the lower curves is ∆UT0 , which we set equal to the mechanical work Wdsc performed on thematerial when compressing it from an initial volume V0 to a final volume V .

12

sample concentration [%]20 40 60 80 100

∆U

V→

Vf[J/g

pnipam]

×104

0

1

2

3

4

5

6 0.08 ° C/min0.125 ° C/min0.3 ° C/min

FIG. 7: ∆UV→Vf as function of volume fraction of pNIPAM for 3 different heating rates. The blue cross is 0.08 C/min, thered triangles is 0.125 C/min and the black circles is 0.3 C/min. The heating rate appears to only have a limited effect on themeasured values of ∆UV→Vf .