Scanning Probe Microscopy of Polymers - American Chemical Society

Chapter 16

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on May 19, 2018 | https://pubs.acs.org Publication Date: July 7, 1998 | doi: 10.1021/bk-1998-0694.ch016

Stretching a Network of Entangled Polymer Chains with a Nanotip J. P. A i m éand S. Gauthier C P M O H UniversitéBordeaux I, 351 Cours de la Libération, F-33405 Talence Cedex, France Abstract. Uniaxial extension of a network of entangled linear polymer chains (PDMS) is performed with an AFM. We show that whatever the shape, the size and the fragility of the network created between the tip and the silica grafted surface, the elastic responses always have the same structure just before the point at w h i c h the rupture happens. The molecular weight dependence is also investigated. The elastic responses are very well described with the tube model when the inextensibility is taken into account. Also we show that the capillary forces do have a sizeable effect at a small deformation when our estimation of the number of parallel chains contained in the network is around a hundred.

1-Introduction. Beyond scanning a surface with a nanotip to assess the structure of a surface at the nanometre scale, A F M is also used to probe the sample properties. From that point of view the force - displacement curves and friction measurements are of particular interest to characterize surface modifications [1-8]. Several questions arise about the use of the theory which can be useful i n describing the contact between a nanotip and a sample either soft or hard. The contact mechanic between two elastic solids[9,10], i n which the two materials are considered as continuum elastic medium, is often used [3,11,12,13]. But up to n o w there is no clear experimental evidence that these theories can be called u p to interpret most of the situations encountered w i t h an A F M . Dissipation and plastic deformation may also occur, which i n many cases, make those theories less useful. Besides, a key difficulty with A F M is that the area of contact is an u n k n o w n parameter. Therefore, to interpret the experimental results, several assumptions have to be made which are not easy to verify. Nevertheless, there are ways that can be used to overcome this main difficulty, either because an accurate knowledge of the contact area between

266

©1998 American Chemical Society

Ratner and Tsukruk; Scanning Probe Microscopy of Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1998.


267 the tip and the sample is not required or because a comparison between several kinds of measurements on different samples allows the experimentalist to extract the relevant variations. One approach that has made progress i n removing some uncertainty at the tip-sample interface is increased control over the chemical nature of the two interacting surface species [14,15]. Another tact that minimizes the absence of knowledge on the contact area, is to investigate the influence of the tip velocity on the tribological behavior of grafted surfaces [13,16]. Another key issue is the development of the force microscopes as biological sensors. For this purpose, the force-displacement curves are used as a way to quantify the interaction between host and guest sites [17, 18]. In that case histograms of rupture force are compiled giving the binding energy of the two interacting sites. F o l l o w i n g this aim one can expect to probe the elastic properties at the submicrometre scale and particularly for the case of polymer sample to assess the elastic behavior at the point at which a fracture happens i n the network. The present paper aims to describe complex force-displacement curves i n which a network of entangled linear polymer chain is involved. Because of the remarkable robustness and reproducibility of the elastic response before the rupture happens and the ability of the tube model to describe the elastic response, the whole force curve preceding the second rupture is interpreted within the framework of rubber elasticity. In the first part experimental results and treatment of the data are described, while the second part is devoted to a discussion i n which the tube model introduced by S. F. Edwards takes a central part [19,20]. 2- Experimental results The preparation of the silica surface and of the silica surfaces grafted with polydimethylsiloxanes (PDMS) is given i n detail i n preceding papers [16, 21]. We have chosen P D M S chains that have one function at both ends such that the chains can only be grafted at one or two locations, making for the latter case a bridge onto the silica surface. They are both monofunctional groups w h i c h avoids the possibility of creating a polymer network w i t h chemical cross links. The chemical function is either a methoxy function or a silanol function. The molecular weights are M =27000 (terminated - O C H 3 ) , M = 110000 and M = 310000 (terminated -SiOH). The pretreated silica wafers, after being hydroxylized i n boiling deionized water for 20 m i n , are dipped i n the polydimethylsiloxane solution with a concentration of 2.8 10~ mol/1 ( M = 27000), 7.1 10" mol/1 ( M = 110000) and 2.2 10' mol/1 ( M = 310000). After the reaction, the treated wafers were rinsed with C H 2 C I 2 . W i t h a Nanoscope III [22], the loading-unloading curve is obtained by monitoring the vertical displacement of the sample. The force-displacement curves obtained w i t h this apparatus are widely described i n the recent literature and w i l l not be recalled here [1-3]. w

w

w

3

4

w

4

w


w

268 Cantilever deflection 8

m

(nm)

40

20

0


-20 -

-40

0

200 400 600 800 1000 piezo displacement AZ_ (nm)

Figure 1: Example of multiple rupture obtained with P D M S grafted onto silica.

The initial purpose of these curves was to calibrate the cantilever deflection using a known piezo vertical displacement [22]. A s a consequence, only a limited number of data were available (no more than 512) w i t h a restricted sampling time (lOOps). To overcome these constraints, we built an electronic device which makes elementary algebraic operations. The signal is taken at the output voltage of the photodiode then is recorded o n an oscilloscope (Fluke PM801). The modification allows us to have up to 8000 data points. In figures 1 and 2 the force-displacement curves are displayed which show a complex behavior with several elastic responses and multiple ruptures. These multiple ruptures are never observed when hard surfaces, silica, mica, semiconductors or amorphous polymers are investigated with the nanotip. In this section we shall first give a qualitative description of the force curves, then we describe i n detail the data treatment. The first instability occurs when the vertical displacement of the piezoelectric actuator needed to unstick the tip from the surface is reached. By multiplying the vertical displacement with the announced cantilever stiffness [23], w h i c h may not be the correct one [21, 24], one gets the order of the magnitude of the pull-off force. The magnitude of the pull-off force is sensitive to chemical species [14] and to dissipation processes that might occur during the rupture of the contact [3,10]. After few oscillations [21], the cantilever goes back to its equilibrium position at rest and should keep it when the sample moves further downwards. N o further deflection of the cantilever is expected, because the tip-sample distance is greater than a hundred nanometers and the attractive interaction becomes negligible. Typically for a radius of the tip of 40 n m and an Hamaker constant of 10" Joule, the dispersive V a n der Waals attraction is less than the thermal energy knT [25]. T w o other possibilities must be considered w h e n material makes a bridge between the tip and the grafted surface. One is when a perfect plastic 20



269

flow takes place, i n that case even if a material remains stuck at the tip we don't detect any mechanical response of the cantilever. The other is when the elastic force is not large enough to be detected by the microlever. When the tip is far away from the sample, the cantilever again bends d o w n w a r d w h i c h means that polymers remain grafted at the tip apex whatever the hypothesis we use to describe the part where no mechanical response is detected. The question of an accurate determination of the domain size of the vertical displacement during which again an elastic response is observed is the key point to properly describe the force-displacement curve. The measure of the domain size depends on the sensitivity of the measurement. The criterion we have used is the following, the mechanical response becomes detectable and significant as soon as we are able to measure a slope of 3%o.. Over a piezo vertical displacement of 20 n m , this criterion leads, w i t h an announced cantilever stiffness of 0.58 N m [23], to a sensitivity of 40 p N . The analysis of the data is focused on this part of the force-displacement curve, keeping i n m i n d that the size of the domain during which an elastic response is observed is driven by the criterion described above. Figure 3 gives a sketch of a forcedisplacement curve defining the different lengths used i n the paper. - 1

In figure 2 are reported the typical shapes of the curve observed. The elastic response is non linear as shown with the increase of the slope as a function of the vertical piezo electric displacement. Before going further into the description of the data, it is worth recalling a few results coming from the framework of the continuum theory that describes the contact between two elastic solids i n presence of adhesion. Following the usual analysis of a force displacement curve, i n the linear regime the relationship between the cantilever deflection 8 given by [3]:

m

and the vertical piezoelectric displacement A Z p is

5m = " 1

(1)

+-

where k is the cantilever stiffness, and k the contact stiffness of the sample. For a stiffness k much larger than k the slope is close to one, while for a sample stiffness close to that of the cantilever the slope is equal to 0.5. In addition for a slope smaller or equal to 0.5, close to the instability, a non linear behavior is anticipated and the force-displacement curve ends with a rounded shape indicating that the contact stiffness decreases (figure 4). Here the behavior is non linear but with a convex curvature indicating an increase of the slope as AZp increases, that is just the opposite of what is predicted w i t h the theory describing the contact of a tip with a semi infinite elastic medium. A s a first attempt to better understand the curves, a power law is used to fit the relationship between the cantilever deflection and the elastic displacement of the polymer: m

s

s

m

Ratner and Tsukruk; Scanning 4 Probe Microscopy of Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1998.

270


Cantilever deflection 8

0

(nm)

m

200 400 600 800 piezo displacement A Z (nm)

1000

p

Figure 2 : Experimental force curves showing second ruptures which happen for different vertical displacements and different forces of rupture. For clarity the curve (b) is shifted upward.

k1 ^

L

° > L

L

P

. ! .

5

s

1

6

st

Figure 3: Sketch of a force - displacement curve showing the mean of the different parameters used : Lo is the length necessary to pull the tip out of the surface; L p is the length where no elastic response occurs or is detectable; 8s is the length on which we measure an elastic response; 8 t = Lp + 8 ; p is the slope at the very end of the s

elastic response; 8

m

S

is the cantilever deflection giving the force of rupture f p t = ru

0.58*8 . m

F (nN)

F (nN)

-3-

-20

20

60 AZ (nm)

100

-12L

140

-2

0 AZ (nm) P

Figure 4 : Computed force curves, a) The stiffness of the sample k is larger than the s

one of the cantilever km, b) the stiffnesses k

m

and k are approximately the same [3]. s


271 Om = A 5 s «

(2)

where the elastic displacement of the sample is normally given by 8s = A Z - 8m if the tip is attached at a spring. Because the spring is a microlever built in at one end, any vertical motion of the piezo actuator leads also to a lateral motion of the tip and the elastic displacement of the neck is given by 8s = A Z \ r (1 + tan (8)) - 8 where 6 is the angle made between the cantilever beam and the p

p

2


m /

horizontal plane. For 6 = 12°, this makes a difference of 2.5% with the previous relation. The values of the exponents a obtained for two molecular weights are reported in figure 5. They are centred around the exponent 3 with scattered values on the prefactor A. Therefore, we reduce the number of parameters and fix the exponent equal to 3. Typical results are reported in figures 6. The law with an exponent 3 describes quite well the elastic responses of the large molecular weights ( M = 110000 and 310000) and reasonably well the ones obtained with the lower mass (M =27000). This result indicates that whatever the shape, the fragility and the length of the neck between the surface and the tip, the elastic responses remain identical. This can be shown in a more spectacular way by interpreting the non-linear behavior through consideration about change of the effective sample stiffness. The dimensional analysis tells us that A is the product of the reciprocal of a square length multiplied by the ratio of the stiffness of the neck and of the cantilever stiffness. Therefore it might be interesting to consider an effective stiffness expressed explicitly as a function of the elastic elongation of the polymer neck. We rewrite equation 2 as k 8m = w

w

m

2

k (8 ) 8 with ks(8 ) given by k (8 )= ks° 8s , where k ° is the stiffness of the neck at the beginning of the measurable elastic response. Following this procedure, equation 1 can be used in introducing the measured non linear variation of the sample stiffness: s

8

m

s

S

s

=

s

Z— AZp

s

s

(3)

2

k8s s

or: 8m'=

^ 1+

(AZp-Om')

AZp

(4)

2

where 8m' =^[A 8m and A Z ' = >/AAZp. The coordinate transformation and equation 4 predict that if the elastic response is correctly described with equation 2, the observed elastic responses as a function of the vertical piezoelectric displacement should appear identical. In other words whatever the particular properties of the polymer neck - fragility, stiffness, size which are not controlled in our experimental procedure, all the curves must be p


272 exponent a

o o o -°oo o

•

o

#

oo

o o

0


o •

100

200

300 400 L (nm)

500

600

p

Figure 5 : Exponent a versus the length L . (•) M =27000 and (o) M =110000. p

Cantilever deflection 8 (nm)

w

Cantilever deflection 5 (nm)

m

II 0

w

m

: 50

: 2 is mostly below 5 n N , the sample of M = 110000 exhibiting an intermediate behavior with f t > 5 n N for X around or below 2. A t this stage it is worth to recall that our experimental determination of X is set arbitrarily, but as it was always the same whatever the M and the length of the force-displacement curve, the relative evolutions become meaningfull. Therefore leaving aside the quantitative value of Xmax/ the experimental results show that for the high molecular weight, the force breaking the network does not depend of X , or equivalently (figure 14) within the framework of the tube model does not depend of the tube structure a/b. It is much less evident for the two other molecular weights for which the rupture force decreases with a / b . A l s o it is often suggested that at a high deformation a network of entangled polymer chains may exhibit local crystallisation [20, 27, 28]. If it happens i n the neck, this clearly does not influence the elastic behavior before the rupture. We do not know at what location the rupture occurs, within the neck, for example i n the middle, or either at the interface polymer-surface or polymer-tip. From the force f pt and the corresponding diameter f, a n estimation of the strength of the adhesive energy gives 0.5 J n r suggesting that the network breaks at the interface rather than in the network itself. In any case, wherever the rupture happens the elastic responses observed remain identical.


rU

m a x

s

s

w

w

m

m

w

r u p

m a x

w

m a x

rU

2

Conclusion. The multiple ruptures observed on the force-displacement curves have been interpreted as fractures of an entangled network of P D M S chains created between the nanotip and the silica grafted surface. The elastic responses observed at a high deformation of the network always exhibit the same behavior, whatever the molecular weight as long as it is larger than the mass needed to have an entangled network, and whatever the shape, the fragility and size of the network. The use of the tube model taking into account the inextensibility of the chains is able to reproduce most of the elastic responses observed, thus plays a central part in the interpretation of the elastic responses. A l s o the experimental results bring new information about the respective influence of the force of capillarity with respect to that of the entangled network. From that point of view they might be of some help i n understanding


285

Force (nN)


0

-201 1

1

1

1

1

1

1

2

3

4

5

6

7

1 8

X Figure 15 : Theoretical variations of the force versus X when the Edwards model is used (

) and when a capillarity force f

c a p

is applied. (

) the strength fcap is ten

times larger than the strength of the network f ( S/

) f p is hundred times larger ca

than the f . s

Figure 16 : Measured rupture forces as a function of Xmax- (•) M =27000, (o) w

M = l 1 0 0 0 0 and (ffl) M =310000. w

w


286


fracture in polymer networks or failure of adhesion when linear polymers are involved [31]. Also the elastic behavior of the PDMS network can provide a useful model for more complex systems such as biological macromolecules since it explicitly shows the entropic contribution of the elastic response. Acknowledgements: It is a pleasure to thank Professor M . Fontanille for his collaboration on the general topic "molecules and polymers grafted on silica". We are also very indebted to D. Michel who set the electronic devices and the modifications on the NIII with which the experimental data have been collected. Literature Cited [1] Burnham, N.A.; Colton, R. J. Vac. Sci. Technol. A 1989, 4, 2906. [2] Salmeron, M . MRS Bull. 1993, 18, 20,. [3] A i m é , J. P.; Elkaakour, Z.; Odin, C.; Bouhacina, T.; Michel, D.; Curély, J.; Dautant, A. J. Appl. Phys. 1994, 263, 1720. [4] Overney, R. M.; Meyer, E. M.R.S. Bulletin 1993, 18, 26. [5] Overney, R. M.; Meyer, E.; Frommer, J.; Brodbeck, D.; Lüthi, R.; Howald, L.; Güntherodt, H. J.; Fujihira, M.; Takano, H.; Gotoh, Y. Nature 1992, 359 , 133. [6] Radmacher, M.; Tillman, R. W.; Fritz, M.; Gaub, H . E. Science 1992, 257 , 1900. [7] Singer, L. J. Vac. Sci. Technol. A 1994, 12 , 2605. [8] Frommer, J. E. Thin Solid Films 1996, 273 , 112. [9] Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London 1971, A324 , 301. [10] Maugis D. J. J. Colloid Interface Sci. 1992, 150 , 243. [11] Carpick, R. W.; Agraït, N.; Ogletree, D. F.; Salmeron, M . J. Vac. Sci. Technol. B 1996, 14, 1289. [12] Aimé, J. P.; Elkaakour, Z.; Gauthier, S.,; Michel, D.; Bouhacina, T.; Curély, J. Surf. Science 1995, 329, 149. [13] Tsukruk, V. V.; Bliznyuk, V. N.; Hazel, J.; Visser, D.; Everson, M . P. Langmuir 1996, 12 , 4840. [14] Frisbie, C. D.; Rozsnyai, F. F.; Noy, A.; Wrighton, M.S.; Lieber, C. M . Science 1994, 265 , 2071. [15] Wilbur, J. L.; Biebuck, H . A.; MacDonald, J. C.; Whitesides, G. M . Langmuir1995,11, 825. [16] Gauthier, S.; Aimé, J. P.; Bouhacina, T.; Attias, A . J.; Desbat, B. Langmuir 1996, 12, 5126. [17] Florin, E.; Moy, V.; Gaub, H . Science 1994, 264, 415. [18] Lee, G.; Chrisley, L.; Colton, R.; and al Science 1994, 266, 771. [19] Edwards, S. F.; Vilgis, T. A. Polymer 1986, 27 ,483. [20] Edwards, S. F.; Vilgis, T. A. Rep. Prog. Phys. 1988, 51 , 243. [21] Bouhacina, T.; Michel, D.; Aimé, J. P.; Gauthier, S. J. Appl. Phys. submitted. [22] Digital Instrument (Santa Barbara).



287 [23] For instance, the A F M cantilevers (Nanoprobes). [24] Clevand, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Sci. Instrum. 1993, 64 , 403. [25]Israelachvili,J. N . Intermolecular and Surface Forces ; Acedemic press limited, London, 1985. [26] Pincus, P. Macromolecules 1976, 9 , 386. [27] Treloar, L. R. G. The Physics of Rubber Elasticity ; 2° Ed., Oxford University Press, 1976. [28] Ferry, J. D. Viscoelastic Properties of Polymers ; Wiley; New York, 1970. [29] De Gennes, P. G. Scaling Concepts in Polymer Physics ; Cornell University press; Ithaca and London, 1979. [30] Mazan, J.; Leclerc, B.; Galandrin, N.; Couarraze, G. Eur. Polym. J.. 1995, 31 ,803. Macosko, C. (private communication). [31] Raphaël, E.; De Gennes, P. G. Journal of Phys.Chemistry, 1992, 96, 4002. Ji, H.; De Gennes, P. G. Macromolecules 1993, 26, 520.


Scanning Probe Microscopy of Polymers - American Chemical Society

Recommend Documents